JEE Main - Elastic and inelastic collisions in one and two dimensions Online Test (MCQ Quiz)

1. In a perfectly elastic collision, what is conserved?

A) Momentum only B) Kinetic energy only C) Both momentum and kinetic energy D) Neither momentum nor kinetic energy

2. In a perfectly inelastic collision, what is true about the colliding bodies after impact?

A) They move with different velocities B) They move with the same velocity C) They come to rest D) Their kinetic energy is conserved

3. Which of the following is a characteristic of an inelastic collision?

A) Kinetic energy is conserved B) Total energy is conserved, but kinetic energy is not C) Momentum is not conserved D) The objects stick together after collision

4. If two bodies collide elastically, what is the change in their relative velocity of separation compared to their relative velocity of approach?

A) It is zero B) It is equal in magnitude and opposite in direction C) It is half D) It is double

5. Consider a one-dimensional elastic collision between a moving object of mass m1 and a stationary object of mass m2. If m1 = m2, what happens to the velocities after collision?

A) Both objects stop B) The first object stops, and the second object moves with the initial velocity of the first C) The first object reverses its direction, and the second object remains stationary D) Both objects move with half the initial velocity

6. In a one-dimensional inelastic collision, where a ball of mass m moving with velocity v collides with a stationary ball of mass 2m and they move together, what is the final velocity?

A) v/3 B) 2v/3 C) v D) 3v

7. A ball of mass 2 kg moving at 5 m/s collides head-on with a stationary ball of mass 3 kg. If the collision is perfectly elastic, what is the velocity of the 3 kg ball after collision?

A) 0 m/s B) 2 m/s C) 4 m/s D) 5 m/s

8. During a collision, which quantity is always conserved in the absence of external forces?

A) Kinetic energy B) Linear momentum C) Angular momentum D) Total energy

9. In a two-dimensional elastic collision, a particle of mass m moving with velocity u collides with a stationary particle of mass 2m. If the first particle is deflected by 90 degrees, what is the speed of the second particle after collision?

A) u/3 B) u/2 C) 2u/3 D) u

10. Which type of collision results in the maximum loss of kinetic energy?

A) Perfectly elastic collision B) Perfectly inelastic collision C) Slightly inelastic collision D) Semi-elastic collision

11. A body of mass M moving with velocity V collides with a body of mass m at rest. If the collision is perfectly inelastic, what is the velocity of the combined mass?

A) V * (M / (M+m)) B) V * (m / (M+m)) C) V D) 0

12. In a one-dimensional elastic collision, if the incident particle is much lighter than the target particle, what is the approximate final velocity of the incident particle?

A) Its initial velocity B) Its initial velocity reversed C) Zero D) Half its initial velocity

13. A bullet is fired into a block of wood, and they move together. This is an example of which type of collision?

A) Elastic collision B) Inelastic collision C) Perfectly inelastic collision D) Head-on collision

14. What is the coefficient of restitution (e) for a perfectly elastic collision?

A) e = 0 B) 0 < e < 1 C) e = 1 D) e > 1

15. What is the coefficient of restitution (e) for a perfectly inelastic collision?

A) e = 0 B) 0 < e < 1 C) e = 1 D) e > 1

16. A particle of mass m collides with a stationary particle of mass M. If the collision is elastic and M >> m, what is the velocity of the lighter particle after collision?

A) Approximately its initial velocity B) Approximately its initial velocity in the opposite direction C) Approximately zero D) Approximately half its initial velocity

17. In a two-dimensional inelastic collision, momentum is conserved, but kinetic energy is not. What is the relationship between their initial and final kinetic energies?

A) Initial KE = Final KE B) Initial KE > Final KE C) Initial KE < Final KE D) Initial KE = 0

18. A car of mass 1000 kg moving at 20 m/s collides with a stationary truck of mass 5000 kg. If they move together after collision, what is their common velocity?

A) 3.33 m/s B) 5 m/s C) 10 m/s D) 20 m/s

19. If the relative velocity of separation is equal to the relative velocity of approach, the collision is:

A) Inelastic B) Perfectly inelastic C) Elastic D) Partially elastic

20. Consider a system of two particles undergoing a collision. If no external force acts on the system, the total linear momentum of the system:

A) Is always conserved, regardless of the type of collision B) Is conserved only in elastic collisions C) Is conserved only in inelastic collisions D) Is never conserved during a collision

21. In a one-dimensional elastic collision, a particle of mass m1 moving with velocity u1 collides with a particle of mass m2 moving with velocity u2. If u1 = u2, what is the relative velocity after collision?

A) u1 - u2 B) u2 - u1 C) 0 D) u1 + u2

22. A 5 kg ball moving at 10 m/s collides with a 10 kg ball moving at -5 m/s. If the collision is perfectly inelastic, what is the velocity of the combined mass?

A) -1.67 m/s B) 0 m/s C) 2.5 m/s D) 5 m/s

23. What does the coefficient of restitution (e) quantify?

A) The conservation of momentum B) The ratio of kinetic energy after to before collision C) The ratio of relative velocity of separation to relative velocity of approach D) The total energy of the system

24. In a two-dimensional elastic collision, if the incident particle is stationary and the target particle moves off with velocity v, what is the velocity of the incident particle after collision?

A) Zero B) v C) v/2 D) Cannot be determined without masses

25. Which statement is true for any collision between two particles in an isolated system?

A) Kinetic energy is conserved. B) Momentum is conserved. C) Both kinetic energy and momentum are conserved. D) Neither kinetic energy nor momentum is conserved.

26. A body of mass m1 moving with velocity v1 collides with a body of mass m2 moving with velocity v2. If the collision is elastic, the change in kinetic energy of the system is:

A) Always zero B) Non-zero if v1 and v2 are different C) Zero only if m1 = m2 D) Zero only if v1 = v2

27. In a one-dimensional elastic collision, if a heavy object strikes a light object at rest, the light object moves off with approximately:

A) Twice the velocity of the heavy object B) The same velocity as the heavy object C) Half the velocity of the heavy object D) Zero velocity

28. A particle of mass 2 kg moving at 4 m/s collides with a stationary particle of mass 4 kg. If the collision is perfectly inelastic, what is the velocity of the system after collision?

A) 1 m/s B) 2 m/s C) 4/3 m/s D) 0 m/s

29. What happens to the kinetic energy in a partially elastic collision?

A) It is completely lost. B) It is completely conserved. C) It is partially lost. D) It is partially gained.

30. In a two-dimensional elastic collision, a particle A hits a stationary particle B. After collision, A moves at an angle θ with respect to its initial direction and B moves at an angle φ. What is the relationship between θ and φ?

A) θ + φ = 90° B) θ + φ = 180° C) θ = φ D) θ = 2φ

31. Which principle is fundamental to analyzing collisions?

A) Conservation of energy B) Conservation of linear momentum C) Conservation of angular momentum D) Newton's third law

32. A ball of mass m moving with velocity v strikes a wall elastically. What is the change in momentum of the ball?

A) mv B) -mv C) 2mv D) 0

33. In a one-dimensional collision between two identical particles, if the collision is elastic and one particle is initially at rest, what is the velocity of the second particle after collision?

A) Zero B) The initial velocity of the first particle C) Half the initial velocity of the first particle D) The initial velocity of the first particle reversed

34. A body moving with velocity u collides inelastically with a stationary body of the same mass. What is the velocity of the system after collision?

A) u/2 B) u C) 0 D) 2u

35. If a collision is neither perfectly elastic nor perfectly inelastic, it is called:

A) A head-on collision B) A glancing collision C) A partially elastic collision D) A central collision

36. In a two-dimensional elastic collision, if the initial momentum is p, what is the magnitude of the total momentum after collision?

A) p B) p/2 C) 2p D) 0

37. A particle of mass m moving with velocity 2î m/s collides with a stationary particle of mass 2m. If the collision is perfectly elastic and the first particle recoils with velocity -î m/s, what is the velocity of the second particle?

A) 1 î m/s B) 2 î m/s C) 3 î m/s D) 4 î m/s

38. In a one-dimensional perfectly inelastic collision, the kinetic energy is lost primarily in the form of:

A) Heat and sound B) Potential energy C) Work done against friction D) Work done in deformation

39. Which condition must be met for a collision to be considered elastic?

A) Momentum is conserved. B) Kinetic energy is conserved. C) Both momentum and kinetic energy are conserved. D) The objects stick together.

40. A body of mass m collides with a stationary body of mass 3m. If the collision is elastic and the first body rebounds with velocity v/2, what is the velocity of the second body after collision?

A) v/2 B) v/3 C) v/6 D) v

41. In a two-dimensional collision, if the initial velocities of the particles are along the x-axis, what is conserved along the y-axis in the absence of external forces?

A) Kinetic energy B) Momentum C) Angular momentum D) Total energy

42. If a particle of mass m collides with a stationary particle of mass M, and M is very large compared to m (M >> m), in an elastic collision, the velocity of the lighter particle after collision is approximately:

A) Its initial velocity B) Its initial velocity in the opposite direction C) Zero D) Half its initial velocity

43. In a one-dimensional inelastic collision, the loss of kinetic energy is given by:

A) 1/2 * (m1*m2)/(m1+m2) * (v1_initial - v2_initial)^2 B) 1/2 * (m1+m2) * (v_final)^2 C) 1/2 * (m1*v1_initial^2 + m2*v2_initial^2) D) 0

44. What is the ratio of kinetic energy after to before collision for a perfectly elastic collision?

A) 0 B) 1 C) Greater than 1 D) Less than 1

45. A particle of mass m moving with velocity v collides with a stationary particle of mass m. If the collision is elastic, what is the velocity of the first particle after collision?

A) 0 B) v C) v/2 D) -v

46. In a two-dimensional elastic collision, a particle of mass m moving with speed u along the x-axis strikes a stationary particle of mass M. If after collision, the first particle moves at 30 degrees and the second at 60 degrees with the x-axis, what is the ratio of masses m/M?

A) 1/2 B) 1 C) 2 D) 3

47. Consider a system of two particles colliding. Which statement is always true if the net external force on the system is zero?

A) The total kinetic energy of the system is conserved. B) The total linear momentum of the system is conserved. C) The velocity of each particle is conserved. D) The system comes to rest.

48. If a ball of mass 1 kg moving at 10 m/s collides with a stationary ball of mass 3 kg and they move together, what is the kinetic energy of the system after collision?

A) 12.5 J B) 25 J C) 50 J D) 100 J

49. In a one-dimensional elastic collision, if the incident particle has mass m1 and the target particle has mass m2, and m1 < m2, and the target is initially at rest, the final velocity of the incident particle v1' is related to its initial velocity v1 by:

A) v1' = v1 B) v1' = -v1 C) v1' = v1 * (m1 - m2) / (m1 + m2) D) v1' = v1 * (m2 - m1) / (m1 + m2)

Elastic and inelastic collisions in one and two dimensions - Online Test

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