An open knife edge of mass M is dropped from a height h on a wooden floor. If the blade penetrates a distances into the wood, the average resistance offered by the wood to the blade is :-

Options

A. Mg
B. `Mg(1+h/s)`
C. `Mg(1-h/s)`
D. `Mg(1+h/s)^2`

Answer

B

Explanation

Suppose F be the resistive force of wooden plank. It should oppose the weight of the body. Resultant force opposite to the motion =F - Mg
Work done =(F-Mg) s=kinetic energy
Velocity of fall = `sqrt(2gh)`
`therefore (F-mg)s =1/2 M(sqrt(2gh))^2`
or `(F-Mg)s=1/2 M xx 2gh`
or `F=(Mgh)/s + Mg =Mg(1+h/s)`