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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
A rod of mass M and length l is suspended freely from its endandit canoscillate in the vertical plane about the point of suspension. It is pulled to one side and then released. It passes through the equilibrium position withangular speed `omega` . What is the kinetic energy while passing through the mean position ?A. `Ml^(2)omega^(2)`B. `Ml^(2)omega^(2)//4`C. `Ml^(2)omega^(2)//6`D. `Ml^(2)omega^(2)//12` |
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Answer» Correct Answer - C |
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| 2. |
A small ball is suspended from a point O by a light thread of length l. Then the ball is drawn aside so that thread deviates through an angle `theta` from the vertical and set in motion in a horizontal direction at right angles to the vertical plane in which the thread is located. What is the initial velocity that has to be imparted to the ball so that it could deviate through the maximum angle `pi//2` in the process of motion? |
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Answer» Correct Answer - `[sqrt(2glsectheta)]` |
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| 3. |
A uniform rod AB of mass M is placed in contact. with a second rod BC of mass m = M/2 on a horizontal smooth table at right angles to each other as shown in figure-5.141. Find the initial velocity of BC and kinetic energy generated in it ifan impulse 7 is imparted to |
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Answer» Correct Answer - `"["2I//3m, 5I^(2)//3m"]"` |
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| 4. |
A uniform rod of length `1 m` and mass `2 kg` is suspended. Calculate tension `T` (in `N`) in the string at the instant when the right string snaps `(g = 10 m//s^(2))`. |
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Answer» Correct Answer - [(mg)/(4)] |
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| 5. |
AB and CD are two indential rods each of length L and mass M joined to from a cross. Find the M.L of the system about a bisector of the angel between the rods (XY): A. `(ML^(2))/(12)`B. `(ML^(2))/(6)`C. `(ML^(2))/(3)`D. `(4ML^(2))/(3)` |
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Answer» Correct Answer - A |
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| 6. |
A uniform rod of mass m and length l makes a constant angle `theta` with an axis of rotation which passes through one end of the rod. Its moment of inertia about this axis isA. `(ml^(2))/(3)`B. `(ml^(2))/(3) sin theta`C. `(ml^(2))/(3) sin^(2) theta`D. `(ml^(2))/(3) cos^(2) theta` |
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Answer» Correct Answer - C |
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| 7. |
The moment of inertia of cylinder of radius a, mass M and height h about an axis parallel to the axis of the cylinder and distance b from its centre is :A. `(1)/(2)M(a^(2)+2b^(2))`B. `(1)/(2)M(2a^(2)+b^(2))`C. `(1)/(2)M(a^(2)+b^(2))`D. `(1)/(2)M(a^(2)/(3)+(b^(2))/(12))` |
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Answer» Correct Answer - A |
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| 8. |
In the previous question the smallest kinetic energy at the bottom of the incline will be achieved byA. The solid sphereB. The hollow sphereC. The discD. All will achieve same kinetic energy |
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Answer» Correct Answer - D |
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| 9. |
A body is rotating uniformly about a vertical axis fixed in an inertial frame. The resultant force on a particle of the body not on axis isA. VerticalB. Horizontal andskewwiththeaxisC. Horizontal andintersecting theaxisD. None ofthese. |
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Answer» Correct Answer - C |
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| 10. |
The moment of inertia of a uniform semicircularwire of mass M and radius r about a line perpendicular to the plane of the wire through the centre is :A. `Mr^(2)`B. `(1//2)(Mr^(2))`C. `1//4(Mr^(2))`D. `2//5(Mr^(2))` |
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Answer» Correct Answer - A |
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| 11. |
A solid uniform sphere, with radius R = 0.2 m and mass M=50kg,is at rest in an inertial reference frame in deep space. A bullet with mass w = 20 gm and a velocity v= 400 m/s strikes the sphere along the line shownin figufe-5.137, and rapidly comes to rest within the sphere at point P. Determine the subsequent motion of the sphere and the embedded bullet. |
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Answer» Correct Answer - `"["v=0.16 m//s, omega=1.0 rad//sec"]"` |
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| 12. |
A body is uniformly rotating bout an axis fixed in an inertial frame of reference. Let `vecA` be a unit vector along the axis of rotation and `vecB` be the unit vector along the resultant force on a particle P of te ody away from the axis. The value of `vecA.vecB` isA. 1B. `-1`C. 0D. None of these |
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Answer» Correct Answer - C |
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| 13. |
Let `I_1 and I_2` be the moments of inertia of two bodies of identical geometrical shapek, the first made of aluminium and the second of iron.A. `i_(1)ltI_(2)`B. `I_(1)=I_(2)`C. `I_(1)gtI_(2)`D. Relation between `I_(1)` and `I_(2)` depends on the actual shapesofthe bodies. |
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Answer» Correct Answer - A |
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| 14. |
Only under gravity and some initial impulsea sphere cannot roll without sliding on :A. A smooth horizontal surfaceB. A smooth inclined surfaceC. A rough horizontal surfaceD. A rough inclined surface |
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Answer» Correct Answer - B |
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| 15. |
A sphere can roll without slipping on a surface inclined at an angle `theta` if the fiiction coefficient is more than (2/7)g sin `theta` Suppose the friction coefficient is (l/7)g sin `theta` If a sphere is released from rest on this incline then which ofthe following are possible situations:A. It will stay at restB. Itwill make pure translational motionC. It will translate and rotate about the centreD. The angular momentum of the spheres about its centre will remain constant |
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Answer» Correct Answer - C |
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| 16. |
A sphere and circular disc of same mass and radius are allowed to roll down an inclined plane from the same height without slipping. Find the ratio of times taken by these two to come to the bottom of incline :A. `sqrt(14):sqrt(15)`B. `15: 14`C. `sqrt(2) :1`D. `7: 9` |
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Answer» Correct Answer - A |
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| 17. |
A sphere of outer radius `R` having some cavity inside is allowed to roll down on an incline. The incline is then made smooth by waxing and the sphere is allowed to slide without rolling and now the speed attained is `(5//4)v_0`. What is the radius of gyration of the sphere about an axis passing through its centre ?A. `sqrt((2)/(5)) R`B. `(3R)/(4)`C. `(4R)/(5)`D. `sqrt((2)/(3) R` |
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Answer» Correct Answer - B |
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| 18. |
A wheel initially at rest, is rotated with a uniform angular acceleration. The wheel rotates through an angle` theta_(1)` in first one second and through an additional angle `theta_(2)` in the next one second. The ratio `theta_(2)//theta_(1)` is :A. 4B. 2C. 3D. 1 |
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Answer» Correct Answer - C |
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| 19. |
In rear wheel drive cars the engine rotastes the rear whel and the front wheels rotates only becomes the car moves. Ilf such a car accelerates on horizontal road the frictionA. On the rear wheels is in the forward directionB. On the front wheels is in the backward directionC. On the rear wheels has larger magnitude than the frictionD. On the car is in the backard direction |
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Answer» Correct Answer - A::B::C |
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| 20. |
A person is sitting near the edge fo a rotating platfrom when he walks towards the centere, then:A. Moment ofinertia ofsystem increasesB. Angular velocity ofplatform decreasesC. Angular velocity ofplatform increasesD. Angular velocity of platform remains unchanged |
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Answer» Correct Answer - C |
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| 21. |
A hollow sphere of radius `R` and mass `m` fully filled with water of mass `m`. It is rolled down a horizontal plane such that its centre of mass moves with a velocity `v`. If it purely rolls.A. Kinetic energy of the sphere is 5/6 `mv^(2)`B. kinetic energy of the sphere is 4/5 `mv^(2)`C. Angular momentum of the sphere about a fixed point on ground is 8/3 mvRD. Angular momentum of the sphere about a fixed point on ground is 14/5 mvR |
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Answer» Correct Answer - C |
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| 22. |
A simplified model of a bicycle of mass M has two tires that each comes into contact with the ground at a point. The wheel base of this bicycle is JV, and the centre of mass C of the bicycle is located mid way between the tires and a height h above the ground.The bicycleis moving to the right,but slowing down at a constant acceleration a. Air resistance may be ignored. Assuming that the coefficient of sliding friction between each tyre and the ground is ` mu` and that both tyres are skidding (sliding without rotating). Express your answer in terms of w,h,M and g . What is the maximum value of a so that both tyres remain in contact with the ground ? A. `(Wg)/(h)`B. `(Wg)/(2h)`C. `(hg)/(2W)`D. `(h)/(2Wg)` |
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Answer» Correct Answer - B |
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| 23. |
A simplified model of a bicycle of mass M has two tires that each comes into contact with the ground at a point. The wheel base of this bicycle is JV, and the centre of mass C of the bicycle is located mid way between the tires and a height h above the ground.The bicycleis moving to the right,but slowing down at a constant acceleration a. Air resistance may be ignored. Assuming that the coefficient of sliding friction between each tyre and the ground is ` mu` and that both tyres are skidding (sliding without rotating). Express your answer in terms of w,h,M and g . What is the maximum value of `mu` so that both tires remain in contact with the ground : A. `W//2h`B. `h//2W`C. `2h//W`D. `W//h` |
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Answer» Correct Answer - A |
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| 24. |
A uniform circular disc of mass 2 m and radius R placed freely on a horizontal smooth surface as shown in the figure- 5.116.A particle of mass m is connected to the circumference of the disc with a massless string. Now an impulse J is applied on the particle in the directions shown by dotted line. The acceleration of centre of mass of the disc just after application of implues is `("If J "= 10 N -sec ., m=sqrt10 kg and R= 25cm )` A. `1m//s^(2)`B. ` 2m//s^(2)`C. `3 m//s^(2)`D. `4 m//s^(2)` |
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Answer» Correct Answer - D |
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| 25. |
A Stick of length L and mass M lies on a fnctionless horizontal surface on which it is free to move in any way. A ball of mass m moving with speed v collides elastically with the stick as shownin figure-5.115. If after the collision ball comes to rest, then what should be the mass of the ball ? A. `m=2M`B. `m=M`C. `m=M//2`D. `m= M//4` |
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Answer» Correct Answer - D |
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| 26. |
A stick of length `l` lies on horizontal table. It has a mass `M` and is free to move in any way on the table. A ball of mass `m` moving perpendicularly to the stick at a distance d from its centre with speed `v` collides elastically with it as shown in figure. What quantities are conserved in the collision ? what must be the mass of the ball, so that it remains at rest immediately after collision? |
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Answer» Correct Answer - `"["(MI^(2))/(12l^(2))"]"` |
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| 27. |
A thin uniform heavy rod of length l hangs from a horizontal axis passing through one end. The initial angular velocity `omega` that must be imparted to it to rotate it through `90^(@)` is : A. `sqrt(g//l)`B. `sqrt(3g//l)`C. `sqrt((2g//l)`D. `sqrt(6g//l)` |
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Answer» Correct Answer - B |
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| 28. |
The angular velocity of the engine (and hence of the wheel) on a scooter is proportional to the petrol input per second. The scooter is moving on a frictionless road with uniform velocity. If the petrol input is increased by 10% the linear velocity of the scooter is increased byA. `50%`B. `10%`C. `20%`D. `0%` |
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Answer» Correct Answer - D |
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| 29. |
A closed cylindrica tube containing some water (not filling the entire tube) lies in a horizontal plane. If the tueb is rotated about a perpendicular bisector, the moment of inertia of water about the axisA. IcreasesB. DecreasesC. Remains constantD. Increases if the rotation is clockwise and decreases if it is in anticlockwise |
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Answer» Correct Answer - A |
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| 30. |
A smooth sphere A is moving on a frictionless horizontal plane with angular speed `omega` and centre of mass velocity `upsilon`. It collides elastically and head on with an identical sphere B at rest. Neglect friction everywhere. After the collision, their angular speeds are `omega_A and omega_B` respectively. ThenA. `w_(A) lt w_(B)`B. `w_(A) = w_(B)`C. `w_(A) = w`D. `w_(B) = 0` |
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Answer» Correct Answer - C::D |
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| 31. |
Asphere is rotating about adiameter atuniform angular speedthenwhich ofthefollowing options is/arecorrect:A. The particles on the surface ofthe sphere do not have any linear accleration:B. The particles on the diameter mentioned above do not have any linear accelerationC. Different particles on the surface have different angular speedsD. All the speeds on the surface have the same linear speed. |
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Answer» Correct Answer - B |
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| 32. |
In the arrangement shown in figure a weight A possesses mass m, a pulley B possesses mass M. Also known are the moment of inertia I of the pulley relative to its axis and the radii of the pulley R and `2R`. The mass of the threads is negligible. Find the acceleration of the weight A after the system is set free. |
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Answer» Correct Answer - [`(3(M+3m)g)/([M+9m+(I)/(R^(2))])`] |
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| 33. |
A circular plarform is free to rotate in a horizontal plane about a vertical axis passing through its centre. A tortoise is sitting at the edge of the platform. Now, the platform is given an angular velocity `omega_0`. When the tortoise move along a chord of the platform with a constant velocity (with respect to the platform), the angular velocity of the platform `omega(t)` will vary with time t asA. B. C. D. |
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Answer» Correct Answer - B |
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| 34. |
Two identical blocks are placed on as mooth horizontal surface, connected by a light string of length 2I. String touches a fixed smooth pulley at its mid-point initially. Which is attached to two smooth vertical walls as shown in figure-5.127. Blocks is given a speed `V_(0)`perpendicular to string as shown indiagram. B strikes the pulley and stops. . Speed of A when it hits the wall is : A. `(V_(0))/(2)`B. `V_(0)sqrt((3)/(2))`C. `V_(0)`D. `V_(0)sqrt((3)/(8))` |
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Answer» Correct Answer - A |
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| 35. |
A disc of radius R is spum to an angular speed `omega` about its axis and then imported a horiznotal velociy of magnitude `(omega_(0)R)/(4)` (at=t=0) with its plane remaining vertical. The coefficent of friction between the disc and the plane is `mu` The sence of rotation and direction of its lincer speed are shown. in the figure -5.97 choose the correct statement The disc will returen to its intial position : A. if the value of `mult 0.5`B. irrespective of the value of `mu(mugt0)`C. if the value of `0.5ltmult1`D. if `mugt1` |
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Answer» Correct Answer - B |
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| 36. |
A horizontal rotating disc placed on arough surface has an angular speed of 8 rad`//`s when it is lowered on the surface. After 3 seconds, it is observed to have an angular speed of 2.6 rad`//`s. How many revolutions it made from the time of lowering`on the surface until it stops ? Assume the pressure on the surface due to disc is uniform on its area. |
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Answer» Correct Answer - [2.83] |
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| 37. |
Two masses M and m are connect by a light string gong over a pulley of radis r. The pulley is free to rotate about its axis which is kept horizontal. The moment of inertia of the pulley about the axis is I. The system is releaed from rest. Find the angular momentum fo teh system when teh mass Mhas descended through a height h. The string does not slip over the pulley. |
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Answer» Correct Answer - `"["sqrt([2(M-m){M+m+(1)/(r^(2))}r^(2)gh]"]"` |
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| 38. |
A hollow sphere of radius r is rotating about a horizontal axis at some angular speed `omega_(0)`. It is gently lowered to ground and the coefficient of friction between sphere and the ground is `mu`.How far does the sphere move before it starts pure rolling? |
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Answer» Correct Answer - `[(2)/(25)(omega_(0)^(2)r^(2))/(mug)]` |
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| 39. |
Figure shows a horizontal rod AB which is free to rotate about two smooth bearing system. Two identical uniform rods each of mass m are attached to lod AB symmetrically about the centre ofmassO oftherodAB. All the dimensions are given in the figure-5.132. The system is rotating with constant angular velocity co insuch away that the upper rod is coming outward from the plane of the paper in the position shown. Gravity can be assumed to be absent in the experiment, then choose the correct option(s). A. The hinge reaction at A on the rod AB is downwardB. The hinge reaction at B on the rod AB is upwardC. The hinge reaction at B on the rod AB is downardD. The angular momentum of the system about point O is NOT along the rod AB. |
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Answer» Correct Answer - A::B::D |
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| 40. |
If no external force is acting on the system,net linear momentum of the system is conserved.If system is acted upon by some external force,the component of momentum of the system,along which no external force is present or their vector sum is zero,is conserved. If a sharp blow is given to a body its linear momentum changes immediately.Changein angular momentum not only depends on the magnitude of the blow but also on point ofapplication.In the case of symmetrical body we take the axis of rotation through center of the body. A wedge of mass 4m is placed at rest on a smooth horizontal surface. A uniform solids phere of mass m and radiusr is placed at reston the flat portion of the wedge at the point Q as shown in the figure. A sharp horizontal impulse P is given to the sphere at a point below `h=0.4r`from the center of the sphere.The radius of curvature of the curvedportion of the wedge is R.Coefficient off riction to the left side of point Q is `mu` and to the right side of point Q is zero. For a body to rollon a surface without slipping, there should be no relative velocity between the points of contact. Kinetic energy ofthesystem when sphere isatthehighest point is : A. `(P^(2)`)/(10m)`B. `(P^(2)`)/(5m)`C. `(3P^(2)`)/(10m)`D. `(3P^(2)`)/(5m)` |
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Answer» Correct Answer - C |
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| 41. |
If there is no external force acting on a nonrigid body, which of the followhng quantities must remain constant?A. Angular momentumB. LinearmomentumC. Kinetic energyD. Moment ofinertia |
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Answer» Correct Answer - B |
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| 42. |
If no external force is acting on the system,net linear momentum of the system is conserved.If system is acted upon by some external force,the component of momentum of the system,along which no external force is present or their vector sum is zero,is conserved. If a sharp blow is given to a body its linear momentum changes immediately.Changein angular momentum not only depends on the magnitude of the blow but also on point ofapplication.In the case of symmetrical body we take the axis of rotation through center of the body. A wedge of mass 4m is placed at rest on a smooth horizontal surface. A uniform solids phere of mass m and radiusr is placed at reston the flat portion of the wedge at the point Q as shown in the figure. A sharp horizontal impulse P is given to the sphere at a point below `h=0.4r`from the center of the sphere.The radius of curvature of the curvedportion of the wedge is R.Coefficient off riction to the left side of point Q is `mu` and to the right side of point Q is zero. For a body to rollon a surface without slipping, there should be no relative velocity between the points of contact. The maximum height to which the center of mass of the sphere will climb on the curved portion of the wedge is A. `2P^(2)/(5m ^(2)g`B. `(P^(2))/(5m^(2)g)`C. `(P^(2))/(2m^(2)g)`D. None of these |
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Answer» Correct Answer - A |
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| 43. |
A uniform solid cylinder of radius `R=15cm` rolls over a horizontal plane passing into an inclined plane forming an angle `alpha=30^@` with the horizontal(figure). Find the maximum value of the velocity `v_0` which still permits the cylinder to roll onto the inclined plane section without a jump. The sliding is assumed to be absent. |
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Answer» Correct Answer - `[sqrt((1)/(3)gR(7cosalpha-4))]` |
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| 44. |
If the distance of the moon from earth is and the period of revolution is `T_(m)`,then the mass of the earth isA. `(4pi^(2)r_(m)^(2))/(GT_(m))`B. `(4pi^(2)r_(m)^(3))/(GT_(m)^(2))`C. `(4pi^(2)r_(m))/(GT_(m))`D. `(4pi^(2)r_(m))/(GT_(m)^(2))` |
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Answer» Correct Answer - B |
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| 45. |
A horizontal wooden disc of mass 8 kg and diameter 1m is pivoted on frictionless bearing about a vertical axis through its centre.We put a toy train track model in the disc.The track has a negligible mass and average diameter 0.95 ra.The mass ofmodel train is 1.2 kg which can run with a battery.When we switch on the engine the train moves anticlockwise, soon attaining a constant speed of 0.6 m`//`s with respect to the track. Find the magnitude and direction of the angular velocity of the disc relative to the earth. |
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Answer» Correct Answer - [0.27 rad`//`s] |
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| 46. |
A uniform rod AB of length l rotating with an angular velocity `omega` while its centre moves with a linear velocity `v=(omegal)/(6)` If the end A of the rod is suddenly fixed, the angular velocity of A. `(3)/(4)omega`B. `(omega)/(3)`C. `(omega)/(2)`D. `(2)/(3)omega` |
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Answer» Correct Answer - C |
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| 47. |
A weightless rigid rod AB of length / connects two equal masses m one particle is fixed at the end B and the other at the middle ofthe rod as shown in the figure-5.131. The rod can rotate in the vertical plane freely around the hinge point/4. Choose the correct option(s) A. The minimum horizontal velocity required to be given to the particle B so as to make the rod go around in the complete vertical circleisB. The minimum horizontal velocity required to begivento the particle B so as to make the rod go around in the complete vertical circle isC. The ratio of compressive force in the rods AC and BC is 2 : 1 when the masses are at highest point.D. The ratio of compressive force in the rodsA |
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Answer» Correct Answer - A::C |
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| 48. |
If no external force is acting on the system,net linear momentum of the system is conserved.If system is acted upon by some external force,the component of momentum of the system,along which no external force is present or their vector sum is zero,is conserved. If a sharp blow is given to a body its linear momentum changes immediately.Changein angular momentum not only depends on the magnitude of the blow but also on point ofapplication.In the case of symmetrical body we take the axis of rotation through center of the body. A wedge of mass 4m is placed at rest on a smooth horizontal surface. A uniform solids phere of mass m and radiusr is placed at reston the flat portion of the wedge at the point Q as shown in the figure. A sharp horizontal impulse P is given to the sphere at a point below `h=0.4r`from the center of the sphere.The radius of curvature of the curvedportion of the wedge is R.Coefficient off riction to the left side of point Q is `mu` and to the right side of point Q is zero. For a body to rollon a surface without slipping, there should be no relative velocity between the points of contact. Speed ofthe wedge when spherereaches the flat portion again: A. `(2P)/(5m)`B. `(3p)/(5m)`C. `(8P)/(5m)`D. `(P)/(5m)` |
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Answer» Correct Answer - A |
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| 49. |
A man pushes a cylindrical drum through a board of length l as shownin figure-5.109. The drum rolls forward on the ground a distance of `(1)/(2)` There is no slipping at any instant.During the process of pushing the board the distance moved by the man on the ground is : A. `(l)/(2)`B. `(3l)/(4)`C. lD. `(3l)/(8)` |
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Answer» Correct Answer - C |
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| 50. |
A satellite is revolving round the earth. If the universal gravitational constant(G)was decreasing imiformly with time for the satellite, the quantity that still remains constant isA. WeightB. RadiusC. Tangential speedD. Angular momentum |
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Answer» Correct Answer - D |
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