JEE Main · 2026 · 23 Jan 2026 · Shift 1 · Conservation of Momentum

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 temperature (in

^{\circ} C

), if all the heat produced during the collision is retained by these spheres, is :
(specific heat of sphere material

31 cal / kg .^{\circ} C

and

1 cal = 4.2 J

)

Answer: (B)

Solution

In a perfectly inelastic collision the kinetic energy converted to heat is

Δ K E = \frac{1}{2} μ v_{rel}^{2}

, with reduced mass

μ = \frac{m _{1} m _{2}}{m _{1} + m _{2}} = \frac{15 \times 25}{40} = 9.375

kg and relative speed

v_{rel} = 10 + 30 = 40

m/s (opposite directions). Thus

Δ K E = \frac{1}{2} \times 9.375 \times 4 0^{2} = 7500

J. This heat raises the temperature of both spheres:

Δ K E = (m_{1} + m_{2}) S Δ T

with

S = 31 \times 4.2

J kg

^{- 1}^{\circ}

^{- 1}

. Hence

Δ T = \frac{7500}{40 \times 31 \times 4.2} = 1.44^{\circ}

JEE Main · 2026 · 23 Jan 2026 · Shift 1 · Single correct option