Question

A bullet of mass $0.1kg$ is fired on a wooden block to pierce through it, but it stops after moving a distance of $50cm$ into it. If the velocity of the bullet before hitting the wood is $10m{s^{ - 1}}$ and it slows down with uniform deceleration, then the magnitude of effective retarding force on the bullet is ‘$x$’ N. The value of ‘x’ to the nearest integer is?

Answer 1

Hint: In order to solve this question, we will first calculate the retarding acceleration produced on the bullet while piercing through the wooden block using equations of motion, and then using the formula of force we will solve for retarding force acting on the bullet.

Formula used:
Newton’s equation of motion is,
${v^2} - {u^2} = 2aS
where, v is the final velocity of the body, u is the initial velocity of the body, a is acceleration and S is the distance covered by the body.

Complete step by step solution:
We have given that just before hitting the wooden block the initial velocity of the bullet is $u = 10m{s^{ - 1}}$ and it stops after covering a distance of $S = 50cm = 0.5m$ since bullet stops which means final velocity is $v = 0$ let ‘a’ be the acceleration of the bullet so using equation ${v^2} - {u^2} = 2aS$ and putting required values, we get;
$0 - 100 = 2a(0.5) \\
\Rightarrow a = - 100\,m{s^{ - 2}} \\ $
Now, The mass of the bullet is given as $m = 0.1kg$ so the force acting on the bullet is given as $F = ma$ on putting the values, we get
$F = - 0.1 \times 100 \\
\therefore F = - 10N $
It’s given to us that the magnitude of retarding force is $x$ N. So as we found the magnitude of retarding force is $10N$.

Hence, the value of $x$ is $10N$.

Note: It should be remembered that the negative sign of acceleration and force indicates that acceleration is reading in nature which means acceleration is decreasing with time and finally becomes zero and the bullet stops and so the force is retarding in nature.