Question

If a body loses half of its velocity on penetrating $3cm$ 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

Answer: (A)

Let initial velocity of body at point A is v, AB is 3 cm.

From
${\nu }^2=u^2-2as$
${\left(\frac{v}{2}\right)}^2=v^2\cdot 2a\times 3$
$a=\frac{v^2}{8}$
Let on penetrating $3cm$ in a wooden block, the body moves $x$ distance from $B$ to $C$. So, for $B$ to $C$
$u=\frac{v}{2},v=0$
$s=x,a=\frac{v^2}{8}$ (deceleration)
$\therefore (0{)}^2={\left(\frac{v}{2}\right)}^2-2\cdot \frac{v^2}{8}\cdot x$
$x=1$ cm
Note: Here, it is assumed that retardation is uniform.