Hammer of mass N strikes a nail of mass m with a velocity 20 m/s into a fixed wall. The nail penetrates into the wall to a depth of 1 cm. The average resistance of the wall of the pentration of the nail is

Options

A. `((M^(2))/(M+m))xx10^(3)`
B. `(2M^(2))/(M+m)xx10^(4)`
C. `(M+m)/(M^(2))xx10^(2)`
D. `(M^(2))/(M+m)xx10^(2)`

Explanation

From conservation of energy
`m xx v + m(0) = (M + m)v'`
`v' = (M xx 20)/((M +m))`
Average resistance of the wall to the pepnetration the nail is
`F=(M+m)((0^(2)+v'^(2)))/(2xx10^(-2))`
`thereforev^(2)=u^(2)+2as=(M+m)xx(M^(2)xx(20)^(2))/((M+m)^(2))xx(1)/(2xx10^(-2))`
`= (2M^(2))/((M + m)) xx 10^(4)`