Question

A bullet of mass 10 g strikes a wooden block with a velocity of $300m{s^{ - 1}}$. After penetrating 20 cm into it, its velocity drops to$200m{s^{ - 1}}$. Then the average resistance offered by the block is:
$\eqalign{
  & {\text{A}}{\text{.125}}N \cr
  & {\text{B}}{\text{. }}250N \cr
  & {\text{C}}{\text{. }}1250N \cr
  & {\text{D}}{\text{. }}2500N \cr} $

Answer 1

Hint: When a bullet enters a wooden block, it will experience a resistive force or we can say that it will experience retardation. This retardation will reduce its initial velocity and may even take it to rest. So, in order to find the resistance, we just need to find the retardation and retardation times the mass of the bullet will give us the required offered resistance by block.

Formula used:
${v^2} = {u^2} - 2as$
$F = ma$

Complete step by step answer:
When the bullet strikes the wooden block, it will experience a resistive force or we can say that it will experience retardation. This retardation would result in a reduction of the initial velocity of the bullet and might even make the bullet come at rest.
Given:
The mass of the bullet, $m = 10g = 0.01kg$
The initial velocity of the bullet, $u = 300m{s^{ - 1}}$
The final velocity of the bullet, $v = 200m{s^{ - 1}}$
The distance travelled by the bullet during this time, $s = 20cm = 0.2m$

Firstly, let’s find the negative acceleration acting on the bullet when it strikes the wooden block. To find this deceleration use the third law of motion’s mathematical equation, i.e.
${v^2} = {u^2} - 2as \cdots \cdots \cdots \left( 1 \right)$
where ‘v’ represents the final velocity,
‘u’ represents the initial velocity,
‘a’ represents the retardation
and ‘s’ represents the distance traveled inside the wooden block.
Substituting the given values in equation (1), we get:
$\eqalign{
  & {v^2} = {u^2} - 2as \cr
  & \Rightarrow {200^2} = {300^2} - (2a \times 0.2) \cr
  & \Rightarrow 40000 = 90000 - 0.4a \cr
  & \Rightarrow 0.4a = 90000 - 40000 \cr
  & \Rightarrow 0.4a = 50000 \cr
  & \Rightarrow a = \dfrac{{50000}}{{0.4}} \cr
  & \therefore a = 125000m{s^{ - 1}} \cr} $
So, the retardation is $125000m{s^{ - 1}}$ in magnitude but as it is opposite in direction to the displacement of the bullet we have, $a = - 125000m{s^{ - 1}}$

Now, we need to find the resistance. The resistance offered by the wooden block will be nothing but the force applied by it on the bullet. So by Newton’s second law of motion, we have:
$F = ma \cdots \cdots \cdots \left( 2 \right)$
where ‘F’ represents the resistive force,
‘m’ represents the mass of the object
and ‘a’ represents the acceleration.
Substituting the given and calculated value of retardation in equation (2), we get:
$\eqalign{
  & F = ma \cr
  & \Rightarrow F = 0.01 \times - 125000 \cr
  & \therefore F = - 1250N \cr} $
But we are only concerned with the magnitude of the resistance, not its direction which is given by the negative sign.
Thus, the resistance offered by the block is 1250 N and option C is the correct answer.

Note:
Newton’s second law of motion is a very important statement and is used extensively throughout physics. It states that the acceleration of a body as measured from an inertial frame of reference is given by the vector sum of all the forces acting on the particle divided by its mass. Students should not be confused with the presence of the negative sign. The sign only indicates the direction of the force.