Question

An open knife edge of mass '$M$' is dropped from height '$h$' on a wooden floor. If the knife penetrates upto 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 F is the resistance force
the total kinetic energy lost$=$work done by resistance force
$Mg(h+d)=F.d$
$F=\frac{Mg(h+d)}{d}$
$F=Mg(1+\frac{h}{d})$