Question

A shot travelling at the rate of 100 m/s is just able to pierce a plank 4 cm thick. What velocity is required to just pierce a plank 9 cm thick?

• A. 150 m/s
• B. 130 m/s
• C. 245 m/s
• D. 180 m/s

Answer 1

The correct option is A. 150 m/s.

Given,

$v_1=100m/s$

$s_1=4cm$

$s_2=9cm$
As K.E. of shot is spent in doing work against plank resistance $F$

Therefore, $\frac{1}{2}m{v}_1^2=F\times s_1$ and $\frac{1}{2}m{v}_2^2=F\times s_2$
Dividing we get,
$\frac{v_2^2}{v_1^2}=\frac{s_2}{s_1}$
$\frac{v_2}{v_1}=\sqrt{\frac{s_2}{s_1}}=\sqrt{\frac{9}{4}}=\frac{3}{2}$
$v_2=\frac{3}{2}\times v_1=\frac{3}{2}\times 100=150m/s$.