Question

An open knife edge of mass 'm' is dropped from a height 'h' on a wooden

floor. If the blade penetrates upto the depth 'd' into the wood, the average resistance offered by the wood to the knife edge is

• A. mg
• B. $mg(1-\frac{h}{d})$
• C. $mg(1+\frac{h}{d})$
• D. $mg(1+\frac{h}{d}{)}^2$

Answer 1

The correct option is C

$mg(1+\frac{h}{d})$

Let the blade stops at depth d into the wood.

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

$\Rightarrow 0=(\sqrt{2}gh{)}^2+2(g-a)d$

by solving a = $(1+\frac{h}{d})g$

So the resistance offered by the wood = $mg(1+\frac{h}{d})$