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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. |
From a circular disc of radius R and mass 9 M , a small disc of radius R/3 is removed from the disc. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is A. `4MR^(2)`B. `40/9MR^(2)`C. `10MR^(2)`D. `37/9MR^(2)` |
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Answer» Correct Answer - A |
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| 2. |
The moment of inertia of a uniform semicircular disc of mass `M` and radius `r` about a line perpendicular to the plane of the disc through the center isA. `Mr^(2)`B. `1/2Mr^(2)`C. `1/4Mr^(2)`D. `2/5Mr^(2)` |
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Answer» Correct Answer - A |
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| 3. |
A solid homogeneous sphere of mass `M` and radius `R` is moving on a rough horizontal surface partly rolling and partly sliding. During this kind of motion of the sphereA. Total kinetic energy is conservedB. Angular momentum of the sphere about the point of contact is conservedC. Only the rotational kinetic.energy about the center of mass is· conservedD. Angular momentum about the center of mass is conserved |
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Answer» Correct Answer - B |
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| 4. |
Moment of inertia `I` of a solid sphere about an axis parallel to a diameter and at a distance `x` from it varies as:A. B. C. D. |
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Answer» Correct Answer - A |
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| 5. |
`ABC` is a traiangular plate of uniform thickness. The sides are in the ratio shown in the figure. `I_(AB)`, `I_(BC)` and `I_(CA)` are the moments of inertia of the plate about `AB`, `BC` and `CA` repectively. Which one of the following relations is correct? A. `I_(CA)` is maximumB. `I_(AB)gtI_(BC)`C. `I_(BC)gtI_(AB)`D. `I_(AB)+I_(BC)=I_(CA)` |
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Answer» Correct Answer - B |
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| 6. |
A string wrapped around a cyliner of mass `m` and radius `R`. The end of the string is connected to block of same mass hanging vertically. No friction exists between the horizontal surface and cylinder. Acceleration of hanging mass is:A. `g`B. `g/2`C. `g/4`D. `(3g)/4` |
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Answer» Correct Answer - D |
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| 7. |
A string wrapped around a cyliner of mass `m` and radius `R`. The end of the string is connected to block of same mass hanging vertically. No friction exists between the horizontal surface and cylinder. Velocity of hanging block at this moment is:is:A. `sqrt(2piRg)`B. `sqrt(8piRg)`C. `sqrt((piRg)/2)`D. `sqrt(45piRg)` |
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Answer» Correct Answer - D |
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| 8. |
A string wrapped around a cylinder of mass `m` and radius `R`. The end of the string is connected to block of same mass hanging vertically. No friction exists between the horizontal surface and cylinder. Distance moved by hanging mass during the above time interval is:A. `2piR`B. `piR`C. `3piR`D. `(4piR)/3` |
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Answer» Correct Answer - C |
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| 9. |
A string of negligible thicknes is wrapped several times around a cylinder kept on a rough horizontal surface. A man standing at a distance l from the cylinder holds one end of the sitting an pulls the cylinder towards him figure. There is no slipping anywhere. The length of the string passed through the hand of the man whicle the cylinder reaches his hands is A. `l`B. `2l`C. `3l`D. `4l` |
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Answer» Correct Answer - B |
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| 10. |
A solid cylinder of mass `m` rolls on a rough surface with velocity `v_(0)`. It collides elastically with a cubical block of same mass at rest. The centre of mass of both the bodies are at same height. Coefficient of friction between horizontal surface and cylinder as well as horizontal surface and cube is `mu`. No frictional exists between cylinder and cube. The cylinder collides the, cube at `t = 0`, then. Regarding frictional force acting on cylinder we can say that:A. before collision friction acts forwardB. before collision friction does not actC. after collision friction acts backwardsD. after collision friction does not act |
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Answer» Correct Answer - A |
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| 11. |
A solid cylinder of mass `m` rolls on a rough surface with velocity `v_(0)`. It collides elastically with a cubical block of same mass at rest. The centre of mass of both the bodies are at same height. Coefficient of friction between horizontal surface and cylinder as well as horizontal surface and cube is `mu`. No frictional exists between cylinder and cube. The cylinder collides the, cube at `t = 0`, then. Percentage of energy of cylinder lost due to collision is:A. zeroB. `50%`C. `66.67%`D. `33.33%` |
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Answer» Correct Answer - D |
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| 12. |
A solid cylinder of mass `m` rolls on a rough surface with velocity `v_(0)`. It collides elastically with a cubical block of same mass at rest. The centre of mass of both the bodies are at same height. Coefficient of friction between horizontal surface and cylinder as well as horizontal surface and cube is `mu`. No frictional exists between cylinder and cube. The cylinder collides the, cube at `t = 0`, then. Time after which the cylinder starts pure rolling again:A. `(2v_(0))/(3mug)`B. `(v_(0))/(mug)`C. `(2v_(0))/(mug)`D. `(v_(0))/(3mug)` |
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Answer» Correct Answer - D |
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| 13. |
A solid cylinder of mass `m` rolls on a rough surface with velocity `v_(0)`. It collides elastically with a cubical block of same mass at rest. The centre of mass of both the bodies are at same height. Coefficient of friction between horizontal surface and cylinder as well as horizontal surface and cube is `mu`. No frictional exists between cylinder and cube. The cylinder collides the, cube at `t = 0`, then. Velocity of cube when the cylinder starts pure rolling:A. `(v_(0))/2`B. `(v_(0))/3`C. `(2v_(0))/3`D. `(v_(0))/4` |
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Answer» Correct Answer - C |
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| 14. |
A child is standing with folded hands at the center of a platform rotating about its central axis. The kinetic energy of the system is `K`. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now isA. `2K`B. `K//2`C. `K//4`D. `4K` |
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Answer» Correct Answer - B |
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| 15. |
A mass m moving with a constant velocity along a line parallel to the axis, away from the origin. Its anguarl momentum with respect to the originA. is zeroB. remains constantC. goes on increasingD. goes on decreasing |
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Answer» Correct Answer - B |
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| 16. |
A particle is projected with velocity `v` at an angle of `theta` with horizontal. The average angular velocity of the particle from the point of projection to impact equals:A. `(g cos theta)/(thetav)`B. `g/(v sin theta)`C. `g/(v theta)`D. `(g theta)/(v sin theta)` |
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Answer» Correct Answer - D |
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| 17. |
In the figure shown, the plank is being pulled to the right with a constant speed `v`. If the cylinder does not slip then: .A. the speed of the centre of mass of the cylinder is `2v`B. the speed of the centre of mass of the cylinder is zeroC. the angular velocity of the cylinder is `v/R`D. the angular velocity of the cylinder is zero |
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Answer» Correct Answer - C |
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| 18. |
One quarter sector is cut from a uniform circular disc of radius `R`. This sector has mass `M`. It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. It moment of inertia about the axis of rotation is. .A. `1/2MR^(2)`B. `1/4MR^(2)`C. `1/8 MR^(2)`D. `sqrt(2)MR^(2)` |
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Answer» Correct Answer - A |
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| 19. |
A equilaterial triangle `ABC` formed from a uniform wire has two small identical beads initially located at `A`. The triangle is set rotating about the vertical axis `AO`. Then the beads are released from rest simultaneously and allowed to slide down. one long. `AB` and the other along `AC` as shown. Neglecting frictional effects, the quantities that are conserved as the beads slide down, are. . |
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Answer» Correct Answer - B |
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| 20. |
For the given uniform square lamina ABCD, whose centre is O, A. `sqrt(2I)_(AC)=I_(EF)`B. `I_(AD)=3I_(EF)`C. `I_(AC)=I_(EF)`D. `I_(AC)=sqrt(2I)_(EF)` |
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Answer» Correct Answer - C |
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| 21. |
A particle of mass `m=5 kg` is moving with a uniform speed `v=3 sqrt(2)` in the `XOY` plane along the line `Y=X+4`. The magnitude of the angular momentum of the particle about the origin isA. zeroB. 60C. 7.5D. `40sqrt(2)` |
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Answer» Correct Answer - B |
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| 22. |
A particle undergoes uniform circular motion. About which point on the plane of the circle, will the angular momentum of the particle remain conserved?A. centre of the circleB. on the circumference of the circleC. inside the circleD. outside the circle |
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Answer» Correct Answer - A |
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| 23. |
A person sitting firmly over a rotating stool has his arms stretched. If he folds his arms, his angular momentum about the axis of rotationA. increasesB. decreasesC. remains unchangedD. doubles |
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Answer» Correct Answer - C |
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| 24. |
A translational velocity `v_(0)` is imparted in a horizontal direction to a hoop of radius `r` placed on a rough horizontal surface. What is angular velocity of hoop after it stops slipping?A. `(v_(0))/r`B. `(v_(0))/(2r)`C. `(2v_(0))/r`D. `Z``e``r``o` |
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Answer» Correct Answer - B |
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| 25. |
A non-uniform ball of radius R and radius of gyration about geometric centre `=R//2` is kept on a frictionless surface. The geometric centre coincides with the centre of mass. The ball is struck horizontally with a sharp impulse `=J` the point of application of the impulse is at a height `h` above the surface. then.A. the ball will slip on surface for all casesB. the ball will roll purely is `h=(5R)/4`C. the ball will roll purely if `h=(3R)/2`D. there will be no rotation if `h=R` |
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Answer» Correct Answer - B::D |
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| 26. |
Two men each of mass `m` stand on the rim of a horizontal circular disc, diametrically opposite to each other. The disc has a mass `M` and is free to rotate about a vertical axis passing through its centre of mass. Each man start simultaneously along the rim clockwise and reaches their original starting points on the disc. The angle turned through by the disc with respect to the ground (in radian) is:A. `(8mpi)/(4m+M)`B. `(2mpi)/(4m+M)`C. `(mpi)/(M+m)`D. `(4mpi)/(2M+m)` |
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Answer» Correct Answer - A |
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| 27. |
A sphere a ring and a disc of same mass and radius are allowed to roll down three similar sufficiently rough inclined planes as shown in the figure from same height. Which of the follwing order is true for final `KE` of the bodies?A. sphere `gt` disc `gt` ringB. ring `gt` disc `gt` sphereC. disc `gt` ring `gt` sphereD. disc = ring = sphere |
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Answer» Correct Answer - D |
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| 28. |
A force `F` is applied at the top of a ring of mass `M` and radius `R` placed on a rough horizontal surface as shown in figure. Friction is sufficient to prevent slipping. The friction force acting on the ring is: A. `F/2` towards rightB. `F/3` towards leftC. `(2F)/3` towards rightD. Zero |
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Answer» Correct Answer - D |
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| 29. |
A sphere can roll on a surface inclined at an angle `theta` if the friction coefficient is more than `(2)/(7) g sin theta`. Suppose the friction coefficient is `(1)/(7) g sin theta`, and a sphere is released from rest on the incline,A. It will ,tay at restB. It will make pure translational motionC. it will translate and rotate about the centerD. The angular momentum of the sphere about its center will remain constant |
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Answer» Correct Answer - C |
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| 30. |
A cubical block of side L rests on a rough horizonta surface with coefficient of friction `mu`. A horizontal force F is applied on the block as shown. If the coefficient of friction is sufficiently high so that the block does not slide before toppling, the minimum force required to topple the block is A. infinitesimalB. `mg//4`C. `mg//2`D. `mg(1-mu)` |
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Answer» Correct Answer - C |
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| 31. |
A force `F` is applied on the top of a cube as shown in the figure. The coefficient of friction between the cube and the ground is `mu`. If `F` is gradually increased, find the value of `mu` for which the cube will topple before sliding. A. `mugt1`B. `mu lt 1/2`C. `mu gt 1/2`D. `mu lt 1` |
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Answer» Correct Answer - C |
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| 32. |
A block with a square base measuring axa and height `h`, is placed on an inclined place. The coefficient of friction is `m`. The angle of inclination `(theta)` of the plane is gradually increased. The block will.A. topple before sliding if `mugta/h`B. topple before sliding if `multa/h`C. slide before toppling if `mu gt a/h`D. slide before toppling if `mult a/h` |
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Answer» Correct Answer - A::D |
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| 33. |
A uniform rod is kept vertically on a horizontally smooth surface at a point O. IF it is rotated slightly and released, it falls down on the horizontal surface. The lower end will remainA. At `O`B. At a distance less than `l/2` from`O`C. At a distance `l/2` from `O`D. At a distance larger than `l/2` from `O` |
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Answer» Correct Answer - B |
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| 34. |
A ring of mass `M` and radius `R` is released on an inclined as shown. If the coefficient of friction `mu lt 1/2 tan theta`, then during a displacement `l`: A. Acceleration of the ring `=g//2sintheta`B. Acceleration of the ring `=g sin theta-mug costheta`C. work done by the force of friction `=mgl(sintheta-ucostheta)`D. work done by the force of friction is zero |
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Answer» Correct Answer - B |
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| 35. |
A cylinder is rotated clockwise and lowered slowly on arough inclined plane with `(mu=0.8)`. Then: A. cylinder will start going upwardsB. cylinder will start going downwardsC. frictional force will act upwardsD. frictional force will act downwards |
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Answer» Correct Answer - B::C |
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| 36. |
A thin spherical shell of radius `R` lying on a rough horizontal surface is hit sharply and horizontally by a cue. Where should it be hit so that the shell does not slip on the surface?A. `2/3R`B. `5/4R`C. `5/3R`D. `3/2R` |
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Answer» Correct Answer - C |
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| 37. |
The torque `tau` on a body about a given point is found to be equal to AxxL where A is a constant vector, and L is the angular momentum of the body about that point. From this it follows thatA. `dvecL//dt` is perpendicular to `vecL` at all instants to timeB. the component of `vecL` in the direction of `vecA` does not change with time.C. the magnitude of `vecL` does not change with time.D. `vecL` does not change with time. |
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Answer» Correct Answer - A::B::C::D |
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| 38. |
A thin uniform rod `AB` of mass `1kg` move translationally with acceleration `a=2m//s^(2)` due to two antiparallel force as shown. If `l=20cm` then: A. `F_(1)=3N`B. `F_(1)=5N`C. Length of rod is `1m`D. Length of rod is `80cm` |
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Answer» Correct Answer - A::C |
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| 39. |
A time varying force `F = 2t` is applied on a spool as shown in figure. The angular momentum of the spool at time `t` about bottommost point is: A. `(r^(2)t^(2))/R`B. `((R+r)^(2))/r t^(2)`C. `(R+r)t^(2)`D. data is insufficient |
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Answer» Correct Answer - C |
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| 40. |
A uniform thin bar of mass `6 m` and length `12 L` is bend to make a regular hexagon. Its moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of the hexagon is :A. `20mL^(2)`B. `6mL^(2)`C. `12/5mL^(2)`D. `30mL^(2)` |
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Answer» Correct Answer - A |
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| 41. |
A thin uniform rigid rod of length `l` is hinged at one end so that it can move ina vertical plane by rotating about a horizontal axis through upper end. The lower end is given a sharp blow and made to acquire a linear velocity Maximum height attained by lower end of the rod is: A. `(v_(0)^(2))/(3g)` for `v_(0)lt sqrt(6gl)`B. `(3v_(0)^(2))/g` for `v_(0)lt sqrt(6gl)`C. `2l` for `v_(0)ge sqrt(6gl)`D. `l` for `v_(0)=sqrt(3gl)` |
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Answer» Correct Answer - C::D |
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| 42. |
A rod of mass `m` and length `l` is hinged at one of its end `A` as shown in figure. A force `F` is applied at a distance `x` from `A`. The acceleration of centre of mass (a) variea with `x` as: A. B. C. D. |
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Answer» Correct Answer - B |
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| 43. |
The figure shows a uniform rod lying along the `x`-axis. The locus of all the points lying on the `x-y` plane, about which the moment of inertia of the rod is same as that about `O`, is A. CircleB. ParabolaC. Straight lineD. Ellipse |
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Answer» Correct Answer - A |
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| 44. |
A thin rod of mass `m` and length `l` is hinged at the lower end to a level floor and stands vertically. Then its upper end will strike the floor with a velocity given by:A. `sqrt(2gl)`B. `sqrt(3gl)`C. `sqrt(5gl)`D. `sqrt(mgl)` |
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Answer» Correct Answer - B |
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| 45. |
A homogenous rod of length `l=etax` and mass `M` is lying on a smooth horizontal floor. A bullet of mass `m` hits the rod at a distance `x` from the middle of the rod at avelocity `v_(0)` perpendicular to the rod and comes to rest after collision. If the velocity of the farther end of the rod just after the impact is in the opposite direction of `v_(0)` then:A. `eta gt 3`B. `eta lt 3`C. `eta gt 6`D. `eta lt 6` |
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Answer» Correct Answer - D |
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| 46. |
A uniform rod of length `l` is pivoted at point `A`. It is struck by a horizontal force which delivers an impulse `J` at a distance `x` from point `A` as shwon in figure, impulse delivered by pivot is zero if `x` is equal to A. `l/2`B. `l/3`C. `(2l)/3`D. `(3l)/4` |
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Answer» Correct Answer - C |
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| 47. |
Two particle of equal mass `m` at `A` and `B` are connected by a rigid light rod `AB` lying on a smooth horizontal table. An impulse `J` is applied at `A` in the plane of the table and perpendicular at `AB`. The velocity of particle at `A` isA. `J/(2m)`B. `J/m`C. `(2J)/m`D. zero |
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Answer» Correct Answer - B |
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| 48. |
A spool of mass `m` has moment of inertia `I= 2mR^(2)` about its axis of symmetry. The inner and outer radius of spool `R` and `2R` respectively. Thread is wounded onthe inner cylinder and its one end is pulled a force F acting at angle `theta` with horizontal. The surface is sufficiently rough and th.e spool never slides on the surface. For `theta=0^(@)`, the acceletation of spool isA. `F/m`B. `F/(2m)`C. `F/(6m)`D. `F/(3m)` |
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Answer» Correct Answer - D |
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| 49. |
A spool of mass `m` has moment of inertia `I= 2mR^(2)` about its axis of symmetry. The inner and outer radius of spool `R` and `2R` respectively. Thread is wounded onthe inner cylinder and its one end is pulled a force F acting at angle `theta` with horizontal. The surface is sufficiently rough and th.e spool never slides on the surface. Maximum frictional force acting on the spool is:A. `for position 1, spool will rotate clockwiseB. for position 2, spool will hot rotateC. for position 3, spool will rota.te anticlockwiseD. all of the above |
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Answer» Correct Answer - D |
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| 50. |
A spool of mass `m` has moment of inertia `I= 2mR^(2)` about its axis of symmetry. The inner and outer radius of spool `R` and `2R` respectively. Thread is wounded onthe inner cylinder and its one end is pulled a force F acting at angle `theta` with horizontal. The surface is sufficiently rough and th.e spool never slides on the surface. Maximum frictional force acting on the spool is:A. `F/2` towards rightB. `(2F)/3`C. `(5F)/6`D. `F/6` |
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Answer» Correct Answer - B |
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