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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 ball falls vertically onto a floor with momentum `p`, and then bounces repeatedly. If the coefficient of restitution is `e`, then the total momentum imparted by the ball on the floor till the ball comes to rest isA. `p(1+e)`B. `p/(1-e)`C. `p(1+(1)/(e))`D. `p((1+e)/(1-e))` |
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Answer» Correct Answer - D |
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| 2. |
A simple pendulum is supended from a peg on a verticl wall. The pendulum is pulled away from the wall to a horizontal position and releases as shown in figure `-4.152.` The ball hits the wall, the coefficient of restitution being `2//sqrt2.` What is the minimum number of collisions after which the amplitude of oscillation becomes less than `60^(@)` |
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Answer» Correct Answer - `"["4"]"` |
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| 3. |
A closed system consists of two particles of masses `m_1` and `m_2` which move at right angles to each other with velocities `v_1` and `v_2`. Find: (a) the momentum of each particle and (b) the total kinetic energy of the two particles in the reference frame fixed to their centre of inertia. |
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Answer» Correct Answer - `"["(m_(1)m_(2))/(m_(1)+m_(2))sqrt(v_(1)^(2)+v_(2)^(2)),(1" "m_(1)m_(2))/(2m_(1)+m_(2))(v_(1)^(2)+v_(2)^(2))"]"` |
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| 4. |
Two spheres of masses 2m and 3m move towards each other with speed `mu` and v respectively. The centres of the sphere move in the same sraight line. The coeffcient of restitutionis `1//2` Find The condition for which motionof each sphere will be reversedon impect The condition for which each sphere will lose knetic energy on impect. |
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Answer» Correct Answer - `"["2/3lt(mu)/vlt9,9/11ltu/vlt7/3"]"` |
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| 5. |
A projectile of mass 20 kg is fired with a velocity of `400m//s`at an angle of `45^(@)` with the horizontal .At the highest point of the trajectocy the projectile explodes into two fragments of equal mass,one of which falls vertically downward with zero initial speed, The distance of the point where the other fragment falls from the point offiring is:A. 24000 mB. 16000 mC. 32000 mD. 8000 m |
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Answer» Correct Answer - A |
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| 6. |
A shell is fired from a cannot with a speed of `100ms^(-1)` at an anlge `60^(@)` with the horizontal (x-direction). At the highest point of its trajectory the shell explodes into two equal fragments. One of the fragments moves along the negative x-direction with a speed of `50 ms^(-1).` What is the speed of the other fragment at the time of explosion ?A. `150ms^(-1)`B. `50ms^(-1)`C. `100ms^(-1)`D. `200ms^(-1)` |
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Answer» Correct Answer - A |
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| 7. |
A shell is fired from a connot with a velocity V at an angle 0 with the horizontal direction .At the highest point in its path it explodes into two pieces of equal masses. One of the pieces retraces its path to the cannon.The speed of the other piece immediately after the explosion is :A. `3V cos 0`B. `2V cos 0`C. `3/2Vcos 0`D. `V cos 0` |
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Answer» Correct Answer - A |
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| 8. |
A particle is projected with a velocity `200 m//s` at an angle of `60^(@).` At the highest point it explodes into three particle of equal masses. One goes vertically upward with a veloctiy `100m//s` the second particle goes vertically downwards at same speed. What is the velocity of the third particle?A. `200m//s` horizontallyB. `200m//s` with `30^(@)` angleC. `200m//s` horizontallyD. `300m//s` horizontally |
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Answer» Correct Answer - D |
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| 9. |
A block of mass 200 gm is suspended through a vertical spring. The spring is stretched by 1 cm when the block is in equilibrium. A particle of mass 120 gm is dropped on the block from a height of 45 cm. The particle sticks to the block after the impact. Find the maximum extension of the spring. |
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Answer» Correct Answer - `[6.1 cm]` |
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| 10. |
Velocity of a particle of mass `2 kg` change from `vecv_(1) =-2hati-2hatjm/s` to `vecv_(2)=(hati-hatj)m//s` after colliding with as plane surface.A. the angle made by the plane surface with the positive x-axis is `90^(@) + "tan"^(-1)((1)/(3))`B. the angle made by the plane surface with the positive x-axis is `"tan"^(-1)((1)/(3))`C. the direction of change in momentum makes an angle `"tan"^(-1)((1)/(3))`with the `+ve` x-axisD. the direction of change in momentum makes an angle `90^(@) + "tan"^(-1) ((1)/(3))` with the plane surface |
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Answer» Correct Answer - A::C |
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| 11. |
`A 42 kg` girl walks along a stationary uniform beam of mass `21 kg.` She walks with a speed of `0.75 m//s.` What is the speed of the center of mass of the system of girl plus beam ? |
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Answer» Correct Answer - `[0.5m//s]` |
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| 12. |
A particle 1 moving with velocity `v= 10m//s` experienced a head on collision with a stationary particle 2 of the same mass. As a result of collision, the kinetic energy of the system decreased by `50%.` Find the magnitude and direction of the velocity of the particle 1 after collision. |
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Answer» Correct Answer - `[5m//s]` |
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| 13. |
A stream of water droplets, each of mass m = 0.001kg are fired horizontally at a velocity of `10m//s` towards a vertical steel plate where they collide. The droplets one spaced equidistant with a spacing of `1cm.`What is approximate average force exerted on the plate by the water droplets. (Assuming that they do not rebound after collision.)A. 10NB. 100NC. 1ND. 0.1N |
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Answer» Correct Answer - A |
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| 14. |
A bullet moving with a velcity u passes through a plank which is free to move. The two are of equal mass. After pssing through the plank, the velocity of the bullet becomes `fu`. Its velocity relative to the plank now isA. fuB. `(1-f) u`C. `(2f-1) u`D. `(2-f) u` |
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Answer» Correct Answer - C |
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| 15. |
A small block of mass m is pushed towards a movable wedge of mass `etam` and height h with initial velocity u.All surface are smooth. The minimum value of u for which the block will reach the top of the wedge: A. `sqrt(2gh)`B. `etasqrt(2gh)`C. `sqrt(2gh(1+(1)/(eta)))`D. `sqrt(2gh(1-(1)/(eta)))` |
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Answer» Correct Answer - C |
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| 16. |
A plastic ball is dropped from a height of one meter and rebounds several times from the floor. If 1.3 seconds elapse from the moment it is dropped to the second impact with the floor, what is the coefficient of restitution. |
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Answer» Correct Answer - `[0.04]` |
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| 17. |
In the figure shown, the heacvy ball of mass 2m rests on the horizontal surface and the lighter balls of mass m is dropped from a height `hgt2l.` At the instant the string gets taut, the upward velocity of the heavy ball will be : A. `2/3sqrt(gl)`B. `4/3sqrt(gl)`C. `1/3sqrt(gl)`D. `1/2sqrt(gl)` |
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Answer» Correct Answer - A |
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| 18. |
The Atwood machine in figure has a third mass attached to it by a limp string. After being released, the `2m` mass falls a distance x before the limp string becomes laut. Thereafter both the mass on the left rise at the same speed. What is the final speed ? Assume that pulley is ideal. |
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Answer» Correct Answer - `[sqrt((3gx)/(8))]` |
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| 19. |
A wooden block of mass `10g` is dropped from the top of a cliff 100 m high. Simultaneously, a bullet of mass 10 g is fired from the foot of the cliff vertically upwards with a velocity of . `100 m//s` (i) Where and after what time will they meet (ii) If the bullet after striking the block gets embedded in it how high will it rise above the cliff before it starts falling |
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Answer» Correct Answer - `[4.9 m, 77,55 m]` |
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| 20. |
When the KE of a particle is increased by 300%, the momentum of the body si increased by :A. `20%`B. `50%`C. `100%`D. `200%` |
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Answer» Correct Answer - C |
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| 21. |
Masses of the bodies A,B and C are `1` kg, `2` kg and `3` kg respectively. There is no friction between the ground and the bodies. Initially ball A is moving with a avelocity `20` m/s collieds inelhastically `(e=0.5)` with the ball B,which was initially at rest. The ball B further colides elasticaly to the block C (at rest), and then C collides elastically to the will in front. Find the velocities of the three blocks after all collisions occurred. |
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Answer» Correct Answer - `"["v_(A)=9.1m//s,v_(B)=5.7m//s,v_(c)=2.4m//s"]"` |
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| 22. |
The two masses on the right are slightly spearated and initially at rest, the left mass in incident with speed `v_(o)`Assuming head on elestic collisions, (a)if `Mltm,` show that there are exactly two collisions and find all final velocities, if `Mgtm` show that there are three collisions and find all final velocities. |
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Answer» Correct Answer - N//A |
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| 23. |
A particle A of mass m moving on a smooth horizontal surface collides with a stationary particle B of mass 2m directly,situated at a distance d from a wall. The coefficient of restitutionbetween A and B and between B and the wall is e = 1/4. Calculate the distance from the wall where they collide again. Assume that the entire motion takes place along a straight line perpendicular to the wall. |
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Answer» Correct Answer - `[12d//13]` |
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| 24. |
A and B are two identical blocks of same mass `2` m and same physical dimensions as shown in figure `-4.158` A is placed over the block B which is attached to one end of the spring of natural length l and spring contant k. The other end of the speing is attached to a wall. The system is resting on a smooth horizontal surface with the spring in the relaxed state. A small object of mass m moving horizontally with speed v at a height d above the horizontal surface hits the block B along the line of therir cntre of mass in a perfectly elastic collision. There is no friction between A and B. Find the minimum value of v `("say"v_(o))`such that the block A will topple over block B. What is the energy stored in the spring when the blocks A and B returns to their initial position as before collision |
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Answer» Correct Answer - `"["(a)v_(o)=3dsqrt((k/(8m)))(b)zero"]"` |
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| 25. |
Two identical blocks A and B each of mass `2` kg hanging stationsary by a light inextensible flexible string passing over a light and frictionless pulley. A shot C, of mass `1` kg moving vertically with velocity `9` m/s collides with block B and get stuck to it. Calculate : Time after which block B starts moving downwardMaximum height reached by B Loss of mechanical energy upto that instant |
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Answer» Correct Answer - `"["0.9s,0.81m,32.4J"]"` |
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| 26. |
A particle of mass m having collides with a stationary particle of mass M deviated by an angle `pi//2` whereas the particle M recoiled at an angle `theta = 30^(@)` to the direction of theinitial motion of the particle m. How much in percent and in what way has the kinetic energy of this system changed after the collision,if `M/m = 5`. |
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Answer» Correct Answer - `[-40%]` |
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| 27. |
A shell at rest at origin explodes into three fragments of masses 1 kg, 2 kg and m kg. The fragments of masses 1 kg and 2 kg fly off with speeds `12 m//s` along x-axis and `8 m//s` along y- axis. If the m kg piece flies off with speed of `40 m//s` then find the total mass of the shell. |
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Answer» Correct Answer - 3.5 kg |
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| 28. |
A particle of mass M is at rest when it suddenly explodes into there picces of equal massses. One piece flies out along the positive x-axis with a speed of `30`m/s while anotheer goes in the negative y direction with a speed of `20`m/s Find the componenrts of the cvelocity of the third piece. Repeat if the third piecre has a mass `M//2` and the other two each have mass `M//4` |
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Answer» Correct Answer - `"["-30m//s.20m//s,-10m//s"]"` |
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| 29. |
Accordingto a FIR in police station, car A wassittingat rest waiting for a red light at a crossing when it was hit by an identical car B from rear side. Bothcars had their hand brakes on, and from their skid marks it is surmised that they skidded together about `6`m in the oriinal directionof travel before coming to reat. Assuming a stopping force of about `0.7` times the combined weights of the cars (that is, `mu=0.7`) what must have been the approximate speed of car B just before the collision ? |
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Answer» Correct Answer - `"["18.1m//s"]"` |
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| 30. |
A locomotive of mass m starts moving so that its velocity varies according to the law `v=asqrts`, where a is a constant, and s is the distance covered. Find the total work performed by all the forces which are acting on the locomotive during the first t seconds after the beginning of motion. |
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Answer» Correct Answer - `"["1/8"ma"^(4)r^(2)"]"` |
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| 31. |
A flat car of mass `m_(0)` starts moving to the right due to a constant horizontal force `F.S` and spills on the flat car from a stationary hopper. The rate of loading is constant and equal to `mukg//s`. Find the time dependence of the velocity and the acceleration of the flat car in the process of loading. the friction is negligibly small. |
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Answer» Correct Answer - `"["(Ft)/(M(1+(rt)/(M))),F/(M(1+(rt)/(M))^(2)"]"` |
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| 32. |
The centre of mass of a, non uniform rod of length L whose mass per unit length p varies as p =`(kx^(2))/(L)`where k: is a constant and x is the distance of any point from one end, is(from the same end):A. `3/4 L`B. `1/4 L`C. `k/L`D. `(3k)/(L)` |
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Answer» Correct Answer - A |
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| 33. |
A rod of length 1m and mass `0.5 kg` is fixed at one end is initially hanging vertical. The other end is now raised until it makes an angle `60^(@)` with the vertical. How much work is required ? |
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Answer» Correct Answer - `[1.225J]` |
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| 34. |
A platform of infinite mass is moving upward with velocity `5 m//s.` At time t = 0, a ball which is at height 100 m above the platform starts falling freely. The velocity of ball just after the collision will be (Assume elastic collision) `(g=10 m//s^(2)):`A. `40 m//s`B. `50 m//s`C. `20m//s`D. None |
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Answer» Correct Answer - B |
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| 35. |
A ball P of mass `2kg` undergoes an elastic collision with another ball Q at rest. After collision, ball P continues to move in its original direction with a speed one-fourth of its original speed. What is the mass of ball Q ?A. 0.9 kgB. 1.2 kgC. 1.5 kgD. 1.8 kg |
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Answer» Correct Answer - B |
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| 36. |
A cylindrical solid of mass `10^(-2) kg` and cross-sectional area `10^(-4) m^(2)` is moving parallel to its axis (the x-axis ) with a uniform speed of `10^(3) m//s` in the positive direction. At `t = 0`, its front face passes the plane `x = 0`. The region to the right of htis plane is filled with the dust particle of uniform density `10^(-3) kg/m^(3)`. When a dust particles collides with the face of the cylinder, it stricks to its surface. Assuming that the dimensions of the cylinder remain parctically unchanged adn that the dust sticks only to the front face of the cylinder find the x-coordinate of the front of th ecylinder at `t = 150 s`. |
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Answer» Correct Answer - `"["10^(5)m"]"` |
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| 37. |
In which o the following cases the centre of mass of a rod is certainly not at its centre?A. The density continuously increases-from left to right.B. The density continuously decreases from left to righ.C. The density decreases from left to right upto the centre and then increaseD. The density increases from left to right upto the centre and then decrease. |
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Answer» Correct Answer - A::B |
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| 38. |
A force exerts an impulse Ion a particle changing its speed from initial velocity `u` to final velocity `2u`. The applied force and the initial velocity are oppositely oriented along the same line. The work done by the force isA. `3/2 Iu`B. `1/2 IU`C. `IU`D. `2IU` |
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Answer» Correct Answer - B |
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| 39. |
A smooth sphere is moving on a horizontal surface with velocity vector `3hati+hatj` immediately before it hits a vertical wall. The wall is parallel to the vector `hatj` and the coefficient of restitution between the wall and the sphere is `1//3`. The velocity vector of the sphere after it hits the wall is :A. `3hati-1/3 hatj`B. `-hati+hatJ`C. `hati-hatj`D. `-hati-1/3hatj` |
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Answer» Correct Answer - B |
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| 40. |
A child is standing at one end of a long trolley moving with a speed v on a smooth horizontal track. If the child starts running towards the other end of the trolley with a speed u, the centre of mass of the system (trolley + child) will move with a speed :A. ZeroB. `(v+u)`C. `(v-u)`D. v |
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Answer» Correct Answer - D |
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| 41. |
In the figure-4.133 shown A is a ball of mass 2kg fixed at its position and `S_(1), S_(2)` are the walls facing A. Another ball B of mass 4 kg incident on the wall at an angle of incidence `60^(@)` and then successively it collides elastically with wall and as shown in figure-4.132. Trace the locus of centre of mass of the two balls during the motion of the ball B |
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Answer» Correct Answer - `N//A` |
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| 42. |
A uniform solid right circular cone of base radius R is joined to a uniform solid hemisphere of radius R and of the same density, so as to have a common face. The centre of mass of the composite solid lies on the common face. The height of the cone is: A. 1.5RB. `sqrt3 R`C. `3R`D. `2sqrt3 R` |
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Answer» Correct Answer - B |
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| 43. |
A sphere of mass `m_(1)` in motion hits directly another sphere of mass `m_(2)` at rest and sticks to it, the total kinetic energy after collision is `2//3` of their total K.E. before collision. Find the ratio of `m_(1) : m_(2)`.A. `1:1`B. `1:2`C. `2:1`D. `2:3` |
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Answer» Correct Answer - C |
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| 44. |
Two identical balls of equal masses A and B , are lying on a smooth surface as shown in figure Ball A hits the ball B (which is at rest) with a velocity v=16`m//s` What should be the minimum value of coefficient of restitution e beteeen A and B so that B just reaches the highest point of inclined plane: `("Take" g=10 m//s^(2))` A. `2/3`B. `1/4`C. `1/2`D. `1/3` |
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Answer» Correct Answer - B |
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| 45. |
As shown in the figure, a wedge of mass M is placed on a smooth inclined ramp that makes an angle `theta` to the horizontal. An object of mass m rests on top of the wedge. The sliding down the ramp at acceleration a. determine the apparent weight of the objects as it slides down. noth that there is friction between the object and the wedge so that the object remains relatively at rest on the wedge. |
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Answer» Correct Answer - `"["sqrt((2m^(2)ghcos^(2)alpha)/((m+m)(M+msin^(2)alpha)))"]"` |
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| 46. |
AB and CD are two smooth parallel walls. A child rolls a ball along ground from A towards point P find PD so that ball reaches point B after striking the wall CD. Given coefficient of restitution e = 0.5 : A. 0.5 mB. 1.2 mC. 1mD. None of these |
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Answer» Correct Answer - C |
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| 47. |
A wedge of mass m and triangular cross- section (AB = BC = CA = 2R) is moving with a constant velocity `-v hat`I towards a sphere of radius R fixed on a smooth horizontal table as shown in figure. The wadge makes an elastic collision with the fixed sphere and returns along the same path without any rotaion. Neglect all friction and suppose that the wedge remains in contact with the sphere for a very shot time. `Deltat,` during which the sphere exerts a constant force F on the wedge. (a) Find the force F and also the normal force N exerted by the table on the wedge during the time `Deltat.` (b) Ler h denote the perpendicular distance between the centre of mass of the wedge and the line of action of F. Find the magnitude of the torque due to the normal force N about the centre of the wedge, during the interval `Deltat.` |
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Answer» Correct Answer - `"["(2mv)/(Deltat)"("i-1/sqrt3k"),"-[(2mv)/(sqrt3Deltar)+mg]k,rN=(4mvh)/(sqrt3Deltat)"]"` |
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| 48. |
A light particle moving horizontally with a speed of `12 m//s` strikes a very heavy block moving in the same direction at `10 m//s`. The collision is one-dimensional and elastic. After the collision, the particle will A. Move at `2m//s` in its original directionB. Move at `8m//s` in its original directionC. Move at `8m//s` opposite to its original directionD. Move at `12 m//s` opposite to its original direction |
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Answer» Correct Answer - B |
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| 49. |
A ball falls undal gravity from a height of 10m with an initial downward velocity u. It collides with ground, loses halft its energy and then rises back to the same height. Find the initial velocity u. |
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Answer» Correct Answer - `"["14m//s,10m"]"` |
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| 50. |
A disk moving on a frictionless horizontal table collides elastically y with another identical disk as shown. The directions of motion of the two disks make angles 0 and `phi` with the initial line of motion as shown. Then A. `0=30^(@)`B. `0=60^(@)`C. `phi=30^(@)`D. `phi=60^(@)` |
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Answer» Correct Answer - A |
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