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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⁻¹ and 30 m s⁻¹ 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 the sphere material 31 cal kg⁻¹ ° C⁻¹ and 1 cal=4.2 J)

Asked in JEE Main 23rd Jan 1st Shift 2026 · Mechanical work converted into heat

• (1) 1.95
• (2) 1.75
• (3) 1.44
• (4) 1.15

Step-by-step solution

Why the other options are wrong

• (1) comes from no consistent slip lands here; it is a filler above the key. The two natural wrong routes are checkable: treating the whole initial kinetic energy 12000 J as heat gives 2.30 °C, and treating the final kinetic energy 4500 J as heat gives 0.86 °C.
• (2) comes from another filler between the key and option 1. Adding the momenta as if the spheres moved the same way gives v=22.5 m s⁻¹ and a loss of only 1875 J, hence 0.36 °C — nowhere near this value.
• (4) comes from using the whole initial kinetic energy, 12000 J, which alone gives 2.30 °C, and then halving it on the vague grounds that "half is lost". The energy actually converted to heat is the full drop, 12000-4500=7500 J.

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