Question

A bullet moving with a speed of $100$ $m{s}^{-1}$ can just penetrate two planks of equal thickness. Then the number of such planks penetrated by the same bullet when the speed is doubled will be:

• A. $4$
• B. $8$
• C. $6$
• D. $10$

Answer 1

The correct option is B $8$

equation of motion can be be applied:$v^2=u^2+2as$, where acceleration is -ve.

Hence $v^2=u^2–2as$.

v(final velocity) = 0.

Therefore, $u^2=2as$.

i.e. s is proportional to $u^2=\frac{s_1}{s_2}=\frac{u_1^2}{u_2^2}$

Therefore, $s_2=\frac{u_2^2}{u_1^2}\times s_1=\frac{{200}^2}{{100}^2}\times 2\left(planks\right)=8planks$