If a body loses half of its velocity on penetrating 3 cm in a wooden block, then how much will it penetrate more before coming to rest? (a) 1 cm (b) 2 cm (c) 3 cm (d) 4 cm

Answer: (a). Constant resistance: distance ∝ KE lost. Half velocity means KE drops to 1/4: 3/4K lost in 3 cm, so 1/4K per 1 cm. Remaining KE K/4 is lost in 1 cm. So the answer is (a) 1 cm.

If a body loses half of its velocity on penetrating 3 cm in a wooden… | JEE Main 2002 (AIEEE)

Q29JEE Main 2002 · AIEEEEasy

Work-Energy Theorem

If a body loses half of its velocity on penetrating $3\text{ cm}$ in a wooden block, then how much will it penetrate more before coming to rest?

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Answer: (a)

Constant resistance: distance $\propto$ KE lost.
Half velocity means KE drops to $\frac{1}{4}$ : $\frac{3}{4}K$ lost in $3\text{ cm}$ , so $\frac{1}{4}K$ per $1\text{ cm}$ .
Remaining KE $\frac{K}{4}$ is lost in $1\text{ cm}$ .
So the answer is (a) $1\text{ cm}$ .

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