Question

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 1

Hint We should know that energy is defined to be a quantitative property which is transferred to an object in order to perform any kind of work. Energy is always a conserved quantity. Based on this concept we can solve the given question.

Complete step by step answer:
Let us consider that the initial velocity is v.
Initial energy is given as = $\dfrac{1}{2}m{v^2}$
Final energy is given as = $\dfrac{1}{2}m{(\dfrac{v}{2})^2} = \dfrac{1}{4}\left( {\dfrac{1}{2}m{v^2}} \right)$
So, the energy lost is given as = $\dfrac{1}{2}m{v^2} - \dfrac{1}{4}\left( {\dfrac{1}{2}m{v^2}} \right) = \dfrac{3}{4}\left( {\dfrac{1}{2}m{v^2}} \right), - - - - - - - - - - (for\;3\;cm)$
So, Remaining energy = $\dfrac{1}{4}\left( {\dfrac{1}{2}m{v^2}} \right)$
Now using unitary method, to get:
$\dfrac{1}{4}\left( {\dfrac{1}{2}m{v^2}} \right)$ $\to 1\;cm\;penetration$

Hence, the correct answer is Option A.

Note To answer this question, the concept of law of conservation of energy is also important. The law states that energy can neither be created nor can it be destroyed, rather it can only be changed from one form to another.