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JEE Main202623 January 2026Morning ShiftPhysicsCenter of Mass, Momentum and CollisionActual

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 ^ C ), if all the heat produced during the collision is retained by these spheres, is : (specific heat of sphere material 31 cal / kg . ^ C and 1 cal =4.2 ~J )

Options

  1. A1.15
  2. B1.75
  3. C1.44
  4. D1.95

Correct answer

C. 1.44

Step-by-step solution

Using conservation of momentum: m₁ v₁ + m₂ v₂ = (m₁ + m₂)v_f where v₂ = -30 m/s (opposite direction). 15(10) + 25(-30) = 40v_f v_f = -15 m/s Initial kinetic energy: KE_i = 1 2 (15)(10)^2 + 1 2 (25)(30)^2 = 750 + 11250 = 12000 J Final kinetic energy: KE_f = 1 2 (40)(15)^2 = 4500 J Heat produced: Q = 12000 - 4500 = 7500 J = 7500 4.2 = 1785.71 cal Temperature rise: T = Q m_ total c = 1785.71 40 31 = 1.44°C

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