Question

Hammer of mass $M$ stricks a nail of mass $m$ with a velocity $20 \, m \, s^{- 1}$ into a fixed wall. The nail penetration into the wall is of the depth of $1 \, cm$ . The average resistance of the wall to the penetration of the nail is

• A. $\left(\frac{M^{2}}{M + m}\right)\times \left(10\right)^{3}$
• B. $\frac{2 M^{2}}{M + m}\times 10^{4}$
• C. $\frac{M + m}{M^{2}}\times 10^{2}$
• D. $\frac{M^{2}}{M + m}\times 10^{2}$

Answer 1

Answer: (B)

By conservation of momentum
$M\times 20=\left(M + m\right)V$
$V=\frac{M}{\left(M + m\right)}\times 20$
By work-energy theorem, $\frac{1}{2} \, \left(M + m\right)V^{2}=f\times \, 1 \, cm$
$\Rightarrow f=\frac{M^{2}}{M + m}\times 2\times 10^{4}N$