JEE Main · 2021 · 18 Mar 2021 · Shift 2 · Conservation of Momentum

An object of mass

m_{1}

collides with another object of mass

m_{2}

, which is at rest. After collision the objects move with equal speeds in the opposite direction. The ratio of the masses

m_{2}

m_{1}

is :

(A) $1 : 1$
(B) $3 : 1$ ✓ Correct
(C) $1 : 2$
(D) $2 : 1$

Answer: (B)

Solution

Let

m_{1}

have initial velocity

u

and

m_{2}

be at rest. After collision, both move with speed

v

in opposite directions. By momentum conservation:

m_{1} u = m_{1} (- v) + m_{2} v

, giving

m_{1} (u + v) = m_{2} v

. By energy conservation (elastic):

\frac{1}{2} m_{1} u^{2} = \frac{1}{2} m_{1} v^{2} + \frac{1}{2} m_{2} v^{2}

, giving

m_{1} u^{2} = (m_{1} + m_{2}) v^{2}

. Solving these:

u = 3 v

and

m_{2} = 3 m_{1}

, so

m_{2} : m_{1} = 3 : 1

. The answer is (B).

JEE Main · 2021 · 18 Mar 2021 · Shift 2 · Single correct option

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

More JEE Main questions on Conservation of Momentum

A uniform bar of length 12 cm and mass $20 m$ lies on a smooth horizontal table. Two point masses m and $2 m$ are moving in opposite directions with same speed of v and in the same plane as the bar, as shown in figure. These masses strike the bar simultaneously and get stuck to it. …
JEE Main 2026View solution →
Given below are two statements:
Statement I: For a mechanical system of many particles total kinetic energy is the sum of kinetic energies of all the particles.
Statement II: The total kinetic energy can be the sum of kinetic energy of the center of mass w.r.t. to the origin and …
JEE Main 2026View solution →
A small bob A of mass m is attached to a massless rigid rod of length 1 m pivoted at point P and kept at an angle of $6 0^{\circ}$ with vertical as shown in figure. At distance of 1 m below point P, an identical bob B is kept at rest on a smooth horizontal surface that extends t …
JEE Main 2026View solution →
In a perfectly inelastic collision, two spheres made of the same material with masses 15 kg and 25 kg, moving in opposite directions with speeds of $10 m / s$ and $30 m / s$ , respectively, strike each other and stick together. The rise in tem …
JEE Main 2026View solution →
A body of mass 14 kg initially at rest explodes and breaks into three fragments of masses in the ratio $2 : 2 : 3$ . The two pieces of equal masses fly off perpendicular to each other with a speed of $18 m / s$ each. The velocity of the heavier fragment is _\ …
JEE Main 2026View solution →
Two blocks of masses 2 kg and 1 kg respectively, are tied to the ends of a string which passes over a light frictionless pulley as shown in the figure below. The masses are held at rest at the same horizontal level and then released. The distance traversed by the centre of mass i …
JEE Main 2026View solution →