Question

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

• A. $1\text{cm}$
• B. $2\text{cm}$
• C. $3\text{cm}$
• D. $4\text{cm}$

Answer 1

The correct option is A $1\text{cm}$

For first part of penetration, by equation of motion,
${\left(\frac{u}{2}\right)}^2=u^2-2a\left(3\right)$
or $3u^2=24a\Rightarrow u^2=8a$ ... (1)
For latter part of penetration,
$0={\left(\frac{u}{2}\right)}^2-2ax$
or $u^2=8ax$ ... (2)
From (1) and (2)
$8ax=8a\Rightarrow x=1\text{cm}$