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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. |
Ball A is about to hit a wall at an angle of incidence of `theta = 30^(@)`. But before hitting the wall it made a head on collision with another identical ball B. The ball B then collides with the wall. The coefficient of restitution for collision between two balls is `e_(1) = 0.8` and that between a ball and the wall is `e_(1) = 0.6`. Find the final velocity of ball B. Initial velocity of A was `u = 5 ms^(-1)`. Neglect friction. `[tan^(-1)((2.25)/(2.34))=44^(@)]` |
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Answer» Correct Answer - `3.24 ms^(-1)` making an angle of `44^(@)` with the normal to the wall |
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| 2. |
A ball moving with velocity `V_(0)`, makes a head on collision with another identical ball at rest. The velocity of incident ball and the other ball after collision is `V_(1)` and `V_(2)` respectively. (a) Using momentum conservation write an equation having `V_(1) and V_(2)` as unknowns. Plot a graph of `V_(1)` vs `V_(2)` using this equation. (b) Assuming the collision to be elastic write an equation for kinetic energy. Plot a graph of `V_(1)` vs `V_(2)` using this equation. (c) The intersection point of the above two graphs gives solution. Find `V_(1) and V_(2)` . (d) In a particular collision, the plot of graphs mentioned above is as shown in figure Find `V_(1) and V_(2)` for this collision. Also write the percentage loss in kinetic energy during the collision. |
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Answer» Correct Answer - `V_(1)=0,V_(2)=V_(0)` (d) `V_(1)=0.5 m//s ;V_(2)=1.5 m//s ;%` loss in KE =37.5 % |
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| 3. |
Two identical thin rods are welded as shown in the fig. B is midpoint of rod CD. Now the system is cut into two parts through its center of mass M. The part AM weights 4 kg. Find the mass of the other part. |
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Answer» Correct Answer - `(20)/(3) kg` |
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| 4. |
Three identical particles are placed on a horizontal smooth table, connected with strings as shown. The particle B is imparted a velocity `V_(0) = 9 m//s` in horizontal direction perpendicular to the line ABC. Find speed of particle A when it is about to collide with C. |
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Answer» Correct Answer - `6 m//s` |
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| 5. |
Two small motors are kept on a smooth table at a separation `L`. The motors have mass `M and 2M` and are connected by a light thread. The motors begin to wrap the thread and thereby move closer to each other. The tension in the thread is maintained constant at F. Find the time after which the two motors will collide. Neglect the dimensions of the motors and their stands. |
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Answer» Correct Answer - `t = sqrt((4MN)/(3F))` |
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| 6. |
A heavy ball of radius R is travelling on a smooth horizontal surface with a velocity of u0 towards left. A horizontally moving small ball of mass m strikes it at a height `(R)/(2)` above the centre while travelling with velocity u towards right. (a) After collision the small ball moves in vertically upwards direction with velocity u. Prove that this can happen only if `u gt sqrt(3)u_(0)` (b) Find the velocity of small ball after collision if the collision is elastic and the balls are smooth. |
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Answer» Correct Answer - (b) `sqrt(u^(2)+3u_(0)^(2)+3u u_(0))` |
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| 7. |
A ball of mass m approaches a heavy wall of mass M with speed 4 m/s along the normal to the wall. The speed of wall before collision is 1m/s towards the ball. The ball collides elastically with the wall. What can you say about the speed of the ball after collision? Will it be slightly less than or slightly higher than 6 m/s ? |
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Answer» Correct Answer - Slightly less than 6 m/s |
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| 8. |
A smooth rope of mas `m` and length `L` lies in a heap on a smooth horizontal floor, with one end attached to a block of mass `M`. The block is given a sudden kick and instantaneously acquires a horizontal velocity of magnitude `V_(0)` as shown in figure 1. As the block moves to right pulling the rope from heap, the rope being smooth, the heap remains at rest. At the instant block is at a distance `x` from point `P` as shown in figure `-2( P` is a point on the rope which has just started to move at the given instant `)`, choose correct options for next three question. The speed of block of mass `M` is |
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Answer» Correct Answer - (i) `v=(Mv_(0))/(M+lamdax)` (ii) `T=(M^(3)v_(0)^(2)lamda)/((M+lamdax)^(3))` |
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| 9. |
A particle of mass m is flying horizontally at velocity u. It strikes a smooth inclined surface and its velocity becomes vertical. (a) Find the loss in kinetic energy of the particle due to impact if the inclination of the incline is `60^(@)` to the horizontal. (b) Can the particle go vertically up after collision if inclination of the incline is `30^(@)` ? |
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Answer» Correct Answer - (a) `K_(loss) = (m u^(2))/(3)` (b) No |
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| 10. |
In the shown figure, pulleys and strings are ideal and horizontal surface is smooth. The block C (mass 2m) is given a horizontal velocity of `V_(0) = 3 m//s` towards right and the entire system is let go. Find the velocity of three blocks, just after the strings regain tension. Mass of A and B are `2m and m` respectively and take `g = 10 m//s^(2)`. |
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Answer» Correct Answer - `V_(A)=(36)/(7)m//s ;V_(B)=(30)/(7) m//s ;V_(C)=(33)/(7)m//s` |
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| 11. |
2n identical cubical blocks are kept in a straight line on a horizontal smooth surface. The separation between any two consecutive blocks is same. The odd numbered blocks `1, 3, 5,.....(2n–1)` are given velocity `v` to the right whereas blocks `2, 4, 6,......2n` are given velocity `v` to the left. All collisions between blocks are perfectly elastic. Calculate the total number of collisions that will take place. |
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Answer» Correct Answer - `(n(n+1))/(2)` |
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| 12. |
(i) Liquid of density `rho` flows at speed `upsilon` along a flexible pipe bent into a semicircle of radius R. The cross sectional area of the pipe is A and its cross sectional radius is small compared to R. Three strings `S_(1), S_(2) and S_(3)` keep the pipe in place. `S_(3)` ties the two ends of the pipe and the other two string have their ends secured at A and B. Strings `S_(1) and S_(2)` are perpendicular to the string `S_(3)`. The entire system is in horizontal plane. Find the tension in the three strings (ii) A car of mass `M` is moving with a velocity `V_(0)` on a smooth horizontal surface. Bullets, each of mass m, are fired horizontally perpendicular to the velocity of the car with a speed `u` relative to the car. After firing n bullets it was found that the car was travelling with velocity `V_(0)` in a direction opposite to its original direction of motion. Assume that mu `lt lt MV_(0)` and also that nm `lt lt M`. Find n in terms of other given parameters. |
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Answer» Correct Answer - (i) `T_(s1)=T_(s2)=T_(s3)=rhoAv^(2)` (ii) `(pi MV_(0))/(m u)` |
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| 13. |
A flexible rope is in the shape of a semicircle ACB with its centre at O. Ends A and B are fixed. Radius of the semicircle is R. The midpoint C is pulled so that the rope acquires V shape as shown in the figure. (a) Make a guess whether the centre of mass of the rope moves closer to O or moves away from it when it is pulled? (b) Calculate the shift in position of the centre of mass of the rope. |
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Answer» Correct Answer - (a) Closer to O (b) `0.03 R` |
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| 14. |
A heavy block A is made to move uniformly along a smooth floor with velocity `V = 0.01` m/s towards left. A ball of mass `m = 50 g` is projected towards the block with a velocity of `u = 100` m/s. The ball keeps bouncing back and forth between the block A and fixed wall B. Each of the collisions is elastic. After the ball has made 1000 collisions with the block and wall each, the distance between the block and the wall was found to be `L = 1.2 m`. Calculate the average force being experienced by the block due to collision at this instant. All collision are instantaneous |
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Answer» Correct Answer - `F ~= 1200 N` |
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| 15. |
(i) A block of mass m moving towards right with a velocity V strikes (head on) another block of mass M which is at rest connected to a spring. The coefficient of restitution for collision between the blocks is e = 0.5. Find the ratio `(M)/(m)` for which the subsequent compression in the spring is maximum. There is not friction. Ball A collides head on with another identical ball B at rest. Find the coefficient of restitution if ball B has 80% of the total kinetic energy of the system after collision. |
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Answer» Correct Answer - (i) `(M)/(m)=1` (ii) `1//3` |
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| 16. |
Two block A and B of equal mass are connected using a light inextensible string passing over two light smooth pulleys fixed to the blocks (see fig). The horizontal surface is smooth. Every segment of the string (that is not touching the pulley) is horizontal. When a horizontal force `F_(1)` is applied to A the magnitude of momentum of the system, comprising of A + B, changes at a rate R. When a horizontal force `F_(2)` is applied to B (`F_(1)` not applied) the magnitude of momentum of the system A + B once again changes at the rate R. Which force is larger `- F_(1) or F_(2)` ? |
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Answer» Correct Answer - `F_(2)` |
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| 17. |
There is a long narrow and smooth groove in a horizontal table. Two identical blocks A and B each of mass m are placed inside the groove at some separation. An ideal spring is fixed to A as shown. Block A is given a velocity `u` to the right and it interacts with B through the spring. (a) What will be final state of motion of the two blocks ? (b) During their course of interaction what is the minimum kinetic energy of the system ? (c) The spring is removed and the two blocks are tied using a mass less string. Now A is set into motion with speed `u`. What will be the final state of motion of the two blocks in this case ? How much kinetic energy is lost by the system ? Where goes this energy ? |
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Answer» Correct Answer - (a) A will be at rest and B will have a velocity u (b) `(m u^(2))/(4)` (c) Both will be travelling with velocity `(u)/(2)`. Loss in `KE=(m u^(2))/(4)` |
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| 18. |
A metal wire having mass M is bent in the shape of a semicircle of radius R and is sliding inside a smooth circular grove of radius R present in a horizontal table. The wire just fits into the groove and is moving at a constant speed V. Find the magnitude of net force acting on the wire. |
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Answer» Correct Answer - `(2)/(pi)=(MV^(2))/(R)` |
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| 19. |
A man stands on a frictionless horizontal ground. He slides a 10 kg block on the surface with a speed of 3 m/s relative the ground, towards a vertical massive wall. The wall itself it moving towards the man at a constant speed of 2 m/s. The block makes a perfectly head on elastic collision with the wall, rebounds and reaches back to the man 3 second after the throw. At the moment the block was thrown, the wall was at a distance of 10 m from the man. (a) Find the mass of the man. (b) Find the ratio of work done by the man in throwing the block to the work done by the wall on the block. |
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Answer» Correct Answer - (a) 90 kg (b) `(1)/(4)` |
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| 20. |
Two particle A and B, of mass `3m and 2m` respectively, are attached to the ends of a light inextensible string which passes over a smooth fixed pulley of negligible mass. After the system is released and A falls through a distance L, it hits a horizontal inelastic table so that its speed is immediately reduced to zero. Assume that B never hits the table or the pulley. Find (a) the time for which A is resting on the table after the first collision and before it is jerked off, (b) the difference between the total kinetic energy of the system immediately before A first hits the table and total kinetic energy immediately after A starts moving upwards for the first time. Explain the loss in kinetic energy. |
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Answer» Correct Answer - (a) `sqrt((8)/(5)(L)/(g))` (b) `(mgL)/(5)` |
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| 21. |
A toy car of mass m is placed on a smooth horizontal surface. A particle of mass 3m is suspended inside the car with the help of a string of length `l`. Initially everything is at rest. A sudden horizontal impulse `I = 2m sqrt(gl)` is applied on the car and it starts moving. (a) Find the maximum angle `q_(0)` that the string will make with the vertical subsequently. (b) Find tension in the string when it makes angle `theta_(0)` with the vertical. |
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Answer» Correct Answer - (a) `theta _(0) = 60^(@)` (b) `T = (2mg)/(sqrt(3))` |
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| 22. |
Two blocks A and B of mass m and `2m` respectively are connected by a light spring of force constant k. They are placed on a smooth horizontal surface. Spring is stretched by a length x and then released. Find the relative velocity of the blocks when the spring comes to its natural length |
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Answer» Correct Answer - `v_(r)=sqrt((3k)/(2m))x` |
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| 23. |
A smooth track, fixed to the ground, is in the shape of a quarter of a circle. Two small blocks of mass `3m and 2m` are released from the two edges `A and B` of the circular track. The masses slide down and collide at centre O of the track. Vertical height of A and B from O is `h = 2m`. Collision is elastic. Find the maximum height (above O) attained by the block of mass 2m after collision |
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Answer» Correct Answer - 2.96 m |
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| 24. |
A simple pendulum is suspended from a peg on a wall which is inclined at an angle of `30^(@)` with the vertical. The pendulum is pulled away from the wall to a horizontal position (with string just taut) and released. The bob repeatedly bounces off the wall, the coefficient of restitution being `e = (2)/(sqrt(5))` Find the number of collisions of the bob with the wall, after which the amplitude of oscillation (meaured from the wall) becomes less than `30^(@)` |
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Answer» Correct Answer - 4 |
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| 25. |
There are 40 identical balls travelling along a straight line on a smooth horizontal table. All balls have equal speed v and each one is travelling to right or left. All collisions between the balls is head on elastic. At some point in time all balls will have fallen off the table. The time at which this happens will definitely depend on initial positions of the balls. Over all possible initial positions of the balls, what is the longest amount of time that you would need to wait to ensure that the table has no more balls? Assume that length of the table is L. |
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Answer» Correct Answer - `(L)/(v)` |
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| 26. |
A particle of mass `1 kg` is moving with a velocity of 200 m/s. An impulsive force of 4 s duration acts on the particle in a direction opposite to its motion. The force fluctuates a little bit around 40 N magnitude and then it dies out in next 4s showing small fluctuations. An oscilloscope records the force as shown. The two oscillating components in the graph are identical except that one is mirror image of the other. Find the magnitude of velocity of particle after the force stops acting. |
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Answer» Correct Answer - 40 m/s |
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| 27. |
Two particles of mass m each are attached to the end of a mass less spring. This dumb-bell is moving towards right on a smooth horizontal surface at speed V with the spring relaxed. Another identical dumb-bell is moving along the same line is opposite direction with the same speed. The two dumb-bells collide head on and collision is elastic. Assuming collisions to be instantaneous, how many collisions will take place ? |
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Answer» Correct Answer - 2 |
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| 28. |
Two spherical bodies of masses m and 5m and radii R and 2R respectively, are released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, the distance covered by smaller sphere just before collision is |
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Answer» Correct Answer - 7.5 R |
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| 29. |
A shell is fired vertically upward with a speed of 60 m/s. When at its maximum height it explodes into large number of fragments. Assume that the fragments fly in every possible direction and all of them have same initial speed of 25 m/s [Take `g = 10 m//s^(2)`] (a) Prove that after the explosion all the fragments will lie on an expanding sphere. What will be speed of the centre of the sphere thus formed – one second after explosion ? (b) Find the radius of the above mentioned sphere at the instant the bottom of the sphere touches the ground. |
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Answer» Correct Answer - (a) 10 m/s (b) 100 m |
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| 30. |
A box of mass M is at rest on a horizontal surface. A boy of mass `m (lt M)` wants to push the box by applying a horizontal force on it. The boy knows that he will not be able to push the box as the coefficient of friction `mu` between his shoes and ground is almost equal to that between the box and the ground. He decides to run, acquire a speed u and then bang into the box. After hitting the box, the boy keeps pushing as hard as possible. What is the maximum distance through which the box can be displaced this way ? |
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Answer» Correct Answer - `(m^(2)u^(2))/(2mug(M^(2)-m^(2)))` |
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| 31. |
Two identical block A and B each having mass m, are connected with a spring of force constant k. The floor is smooth and A is pushed so as to compress the spring by `x_(0)`. The system is released from this position (a) Calculate the maximum speed of the centre of mass of the system during subsequent motion. (b) What is acceleration of the centre of mass at the instant it acquires half its maximum speed ? |
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Answer» Correct Answer - (a) `(1)/(2) sqrt((k)/(m))x_(0)` (b) `(sqrt(3)kx_(0))/(4m)` |
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| 32. |
A smooth ball A travels towards another identical ball B with a velocity u. Ball B is at rest and the impact parameter d is equal to `sqrt(3) R` where `R` is radius of each ball. Due to impact the direction of motion of ball A changes by `30^(@)`. Find the velocity of B after the impact. It is given that collision is elastic |
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Answer» Correct Answer - `(u)/(2)` |
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| 33. |
A dancer leaps off the floor with her centre of mass having a velocity of 5 m/s making an angle of `theta =37^(@)` to the horizontal. At the top of the trajectory the dancer has her legs stretched so that the centre of mass gets closer to head by a vertical distance of `0.25 m`. By how much does the head rises vertically from its initial position ? `[ sin 37^(@) = (3)/(5)]` |
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Answer» Correct Answer - 0.2 m |
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| 34. |
Two particles (A and B) of masses m and 2m are joined by a light rigid rod of length L. The system lies on a smooth horizontal table. The particle (A) of mass m is given a sharp impulse so that it acquires a velocity u perpendicular to the rod. Calculate maximum speed of particle B during subsequent motion. By what angle `theta` will the rod rotate by the time the speed of particle B become maximum for the first time ? |
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Answer» Correct Answer - `(2u)/(3),180^(@)` |
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| 35. |
A man is running along a road with speed u. On his chest there is a paper of mass m and area S. There is a wind blowing against the man at speed V. Density of air is `rho`. Assume that the air molecules after striking the paper come to rest relative to the man. Find the minimum coefficient of friction between the paper and the chest so that the paper does not fall ? |
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Answer» Correct Answer - `mu_(min)=(mg)/(rhoS(V+u)^(2))` |
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| 36. |
Two blocks A and B, each of mass m, are connected by a spring of force constant K. Initially, the spring is in its natural length. A horizontal constant force F starts acting on block A at time `t=0` and at time t , the extension in the spring is seen to be `l`. What is the displacement of the block A in time `t` ? |
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Answer» Correct Answer - `(Ft^(2))/(4m)+(l)/(2)` |
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| 37. |
In order to make a jump straight up, a `60 kg` player starts the motion crouched down at rest. He pushes hard against the ground, raising his centre of mass by a height `h_(0) = 0.5 m`. Assume that his legs exert a constant force `F_(0)` during this motion. At this point, where his centre of mass has gone up by `h_(0)` his feet leave the ground and he has an upward velocity of `v`. Centre of mass of his body rises further by `h = 0.8 m` before falling down [Take `g = 10 m//s^(2)`] (a) Find `v`. (b) Find the normal force applied by the ground on his feet just before he left the ground. |
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Answer» Correct Answer - (a) `4 m//s` (b) `1560 N` |
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| 38. |
Two blocks of masses `m = 2 kg and m = 8 kg` are connected to a spring of force constant `K = 1 kN//m`. The spring is compressed by `20 cm` and the two blocks are held in this position by a string. The system is placed on a horizontal smooth surface and given a velocity `u = 3 m//s` perpendicular to the spring. The string snaps while moving. Find the speed of the block of mass m when the spring regains its natural length. |
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Answer» Correct Answer - 5 m/s |
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| 39. |
A man of mass m is standing on the flat top of a cart of mass `2m`. The length and height of the cart is `L and H` respectively and it is at rest on a smooth horizontal ground. The man starts running from end A, speeds up and jumps out of the cart at point B with a velocity `u` relative to the cart in horizontal direction. Calculate the total horizontal distance covered by the man by the time he lands on the ground. |
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Answer» Correct Answer - `(2)/(3)[L_+musqrt((2H)/(g))]` |
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| 40. |
An observer `O_(1)` standing on ground finds that momentum of a projectile of mass `2 kg` changes with time as `vec(P)_(01) =(4that (i) + 20 t hat(k))kg m//s` Acceleration due to gravity is `vec(g)=(10 hat(k))m//s^(2)` and there is a wind blowing in horizontal direction. Another observer `O_(2)` driving a car observes that momentum of the same projectile changes with time as - `vec(P)_(02)=(8t hat(i)-16 hat(t) hat(j)+20 t hat(k))kg m//s`. Find the acceleration of the car at `t = (1)/(8) s` |
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Answer» Correct Answer - `vec(a)_(car)=-2 hat(i)+2 hat(j)` |
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| 41. |
A platform is kept on a rough horizontal surface. At one end A of the platform there is a man standing on it. The man runs towards the end B and the platform is found to be moving. In which direction will the platform be moving after the man abruptly comes to rest on the platform at B ? |
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Answer» Correct Answer - (To right) |
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