Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. The masses of A, B and C are $m$, $2m$ and $2m$ respectively. A moves towards B with a speed of $9 \mathrm{~m} / \mathrm{s}$ and makes an elastic collision with it. Thereafter B makes a completely inelastic collision with C. All motions occur along same straight line. The final speed of C is:

(D) $3 \mathrm{~m} / \mathrm{s}$

(A) $4 \mathrm{~m} / \mathrm{s}$

(B) $6 \mathrm{~m} / \mathrm{s}$

(C) $9 \mathrm{~m} / \mathrm{s}$

JEE Main · 2021 · 27 Jul 2021 · Shift 1 · Conservation of Momentum

Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. The masses of A, B and C are

m

2 m

and

2 m

respectively. A moves towards B with a speed of

9 m / s

and makes an elastic collision with it. Thereafter B makes a completely inelastic collision with C. All motions occur along same straight line. The final speed of C is:

(A) $4 m / s$
(B) $6 m / s$
(C) $9 m / s$
(D) $3 m / s$ ✓ Correct

Answer: (D)

Solution

For the elastic collision between A and B, apply conservation of momentum and the coefficient of restitution

e = 1

. From

m \times 9 = m v_{A} + 2 m v_{B}

and

v_{B} - v_{A} = 9

, we get

v_{B} = 6 m/s

and

v_{A} = - 3 m/s

. For the completely inelastic collision between B and C, apply conservation of momentum:

2 m \times 6 = (2 m + 2 m) v_{C}

, giving

v_{C} = 3 m/s

JEE Main · 2021 · 27 Jul 2021 · Shift 1 · Single correct option

Practise more: all JEE Main PYQs on Conservation of Momentum →

JEE Main · 2021 · 27 Jul 2021 · Shift 1 · Conservation of Momentum

Solution

More JEE Main questions on Conservation of Momentum