Question

A hammer weighing $2.5kg$ moving with a speed of $1m{s}^{-1}$ strikes the head of the nail driving it $10cm$ into the nail wall. the acceleration during impact and the impulse imparted to wall will be respectively

• A. $-5m{s}^{-2},2.5Ns$
• B. $-10m{s}^{-2},5Ns$
• C. $-7.5m{s}^{-2},3.5Ns$
• D. $-6m{s}^{-2},4Ns$

Answer 1

The correct option is A $-5m{s}^{-2},2.5Ns$

Mass$=2.5kg$
initial speed$=1m/s^2$
S=10cm=0.1m
By $V²-u²=2as$
$0-1=2 \times a \times 0.1$
$-1=0.2\times a$
$a=-1/0.2=-5m/s^2$
Impulse= change in momentum$=m(v-u)$
$=2.5[0-1]$
$=-2.5kgm/s$

$\therefore a=-5m/s^2$ and impulse$=-2.5Kgm/s=2.5Ns$

Hence,

option $\left(A\right)$ is correct answer.