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. $1cm$
• B. $2cm$
• C. $3cm$
• D. $4cm$

Answer 1

The correct option is A

$1cm$

Step 1: List the known values and conditions

Let the initial velocity be $u$.

It is given that the body loses half of its velocity on penetrating $3cm$.

Therefore, the final velocity

$v=\frac{u}{2}$

Displacement, $S=3cm$

Since the velocity is reduced, the acceleration is negative$=-a$

Step 2: Apply the equation of motion for the first penetration

We know the equation of motion,

$v^2=u^2+2aS$

$\Rightarrow$${\left(\frac{u}{2}\right)}^2=u^2-2a\left(3\right)$

$\Rightarrow$ $u^2=4u^2-24a$

$\Rightarrow$ $3u^2=24a$

$\Rightarrow$ $u^2=8a$

Step 3: Estimate the final distance penetrated

For the second case, we have

Initial velocity $=\frac{u}{2}$

Since the body comes to rest, the final velocity $=0$

Therefore, the equation of motion can be written as,

$v^2=u^2+2aS$

$\Rightarrow$$0={\left(\frac{u}{2}\right)}^2-2aS$

$\Rightarrow$$0=u^2-8aS$

$\Rightarrow$$u^2=8aS$

Substituting the value of $u^2$ we get,

$\Rightarrow$$8a=8aS$

$\Rightarrow$ $S=1cm$

Therefore, the body will penetrate $1cm$ more before coming to rest.

Hence, the correct answer is option (A).