An open knife of mass m is dropped from a height h on a wooden floor. If the blade penetrates up to the depth d into the wood. The average resistance offered by the wood to the knife edge is .

Options

A. mg
B. `mg(1-(h)/(d))`
C. `mg(1+(h)/(d))`
D. `mg(1+(h)/(d))^(2)`

Answer

C

Explanation

Let the blade stops at depth d into the wood.
`v^(2)=u^(2)2aS`
`rArr0=(sqrt(2gh))^(2)+2(g-a)d`
by solving `a=(1+(h)/(d))g`
So the resistance offered by the wood
`=mg(1+(h)/(d))`