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

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) ((M2/M + m))× (10)3 (B) (2 M2/M + m)× 104 (C) (M + m/M2)× 102 (D) (M2/M + m)× 102

Tardigrade Admin · Accepted Answer

By conservation of momentum M× 20=(M + m)V V=(M/(M + m))× 20 By work-energy theorem, (1/2) (M + m)V2=f× 1 cm ⇒ f=(M2/M + m)× 2× 104N

Q. 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 $1 c m$ . The average resistance of the wall to the penetration of the nail is

$(\frac{M ^{2}}{M + m}) \times (10)^{3}$

$\frac{2 M ^{2}}{M + m} \times 1 0^{4}$

$\frac{M + m}{M ^{2}} \times 1 0^{2}$

$\frac{M ^{2}}{M + m} \times 1 0^{2}$

By conservation of momentum
$M \times 20 = (M + m) V$
$V = \frac{M}{( M + m )} \times 20$
By work-energy theorem, $\frac{1}{2} (M + m) V^{2} = f \times 1 c m$
$\Rightarrow f = \frac{M ^{2}}{M + m} \times 2 \times 1 0^{4} N$

Q. Hammer of mass M stricks a nail of mass m with a velocity 20ms−1 into a fixed wall. The nail penetration into the wall is of the depth of 1cm . The average resistance of the wall to the penetration of the nail is

(M+mM2​)×(10)3

M+m2M2​×104

M2M+m​×102

M+mM2​×102