Question

A knife of mass $m$ is at a height $x$ from a large wooden block. The knife is allowed to fall freely, strikes the block and comes to rest after penetrating distance $y$. The work done by the wooden block to stop the knife is

• A. $mgx$
• B. $-mgy$
• C. $-mg(x+y)$
• D. $mg(x-y)$

Answer 1

The correct option is C $-mg(x+y)$

We know that work done by all the forces is change in $K.E$
$W_{\text{all}}=\Delta K$
As particle starts from rest and finally is at rest, $\Delta K=0$
$\Rightarrow W_{\text{gravity}}+W_{\text{block}}=0$
$+mg(x+y)+W_{\text{block}}=0$
$W_{\text{block}}=-mg(x+y)$