A body of mass m moving with speed v collides head-on and elastically with a stationary body of mass 2m. The fraction of the initial kinetic energy transferred to the body of mass 2m is
A
8/9
B
1/9
C
2/3
D
4/9
Show the answer
The answer is A.
For a 1-D elastic collision, the struck body moves off at 2m₁v/(m₁ + m₂) = 2v/3. Its kinetic energy is ½(2m)(4v²/9) = (8/9)(½mv²).
B.
1/9 is the fraction of kinetic energy kept by the body of mass m.
C.
2/3 is the ratio of the final speed of 2m to v, not a fraction of energy.
D.
4/9 omits the factor 2 for the mass of the struck body.
NCERT: Class 11 Physics, Chapter 5, Collisions (elastic collisions in one dimension)
Sample 2NEET level
A block of mass 2 kg moving at 3 m/s on a smooth horizontal surface collides head-on and elastically with a stationary block of mass 1 kg. The velocity of the 1 kg block just after the collision is
A
4 m/s
B
1 m/s
C
2 m/s
D
6 m/s
Show the answer
The answer is A.
For a one-dimensional elastic collision with the second body at rest, v₂ = 2m₁u₁/(m₁ + m₂) = (2 × 2 × 3)/3 = 4 m/s. Check: the 2 kg block moves on at 1 m/s, and momentum (6 kg m/s) and kinetic energy (9 J) are both conserved.
B.
1 m/s is the velocity of the 2 kg block after the collision.
C.
2 m/s is the common velocity in a perfectly inelastic collision.
D.
Assumes the 2 kg block stops and gives all its momentum to the 1 kg block, which does not conserve kinetic energy.
NCERT: Class 11 Physics, Chapter 5 (Work, Energy and Power), Collisions in one dimension
Practise Elastic and inelastic collisions
Practice at the level you choose, with the answer after every question; timed tests with the answers when you submit. Every question is verified against NCERT first.