An open knife edge of mass M is dropped from a height 'h' on a wooden floor if the blade penetrates a distance 'S' into the wood 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 resitive force of wooden plank. It should oppose the weight of the body. Resultante force oppositve to the motion `=F-Mg`
Work done `=(F-Mg)s=` kinetic energy
Velocity of fall `=sqrt(2gh)`
`:.(F-mg)s=1/2M(sqrt(2gh))^(2)`
or `(F-Mg)s=1/2Mxx2gh`
or `F=(Mgh)/s+Mg=Mg(1+h/s)`