Answer

Verified

53.7k+ views

**Hint:**In order to solve this problem, we can use the third equation of motion to find the retardation. We know that according to the third equation of motion.

${v^2} = {u^2} + 2as$

Where v is the final velocity, u is the initial velocity, a is the acceleration and s is the distance.

Since force is the product of mass and acceleration we can get the average force of resistance by multiplying this retardation with the mass of the bullet.

**Complete step by step solution:**

It is given that the mass of the bullet is $60\,g$ . Let it be denoted as ${m_b}$ . Thus we can write

$\therefore {m_b} = 60g = 60 \times {10^{ - 3}}kg$

Let initial velocity of the bullet be denoted as u. It is given as $600m/s$ .

$u = 600\,m/s$

The thickness of the fibre, d of the sheet is 200mm

$d = 200mm = 200 \times {10^{ - 3}}m$

We need to find the average resistance offered by the sheet.

When the bullet strikes the fibre sheet it penetrates into the fibre sheet and finally comes to rest.

Thus we can take the final velocity as Zero.

$\therefore v = 0$

Let the retardation that is offered by the sheet be represented as $a$ .

We know that according to the third equation of motion.

${v^2} = {u^2} + 2as$ (1)

Where v is the final velocity, u is the initial velocity, a is the acceleration and s is the distance.

We have a sheet of 200mm thickness. This can be taken as the distance travelled.

Let us substitute all the values in equation 1

Then, we get

$0 = {\left( {600} \right)^2} + 2 \times a \times \left( {200 \times {{10}^{ - 3}}} \right)$ $ \Rightarrow a = - 9 \times {10^5}m/{s^2}$

From Newton's second law we have

$F = ma$

Mass here is the mass of bullet ${m_b}$

On substituting the values we get

$F = - 60 \times {10^{ - 3}} \times 9 \times {10^5}$

$ \Rightarrow F = - 54 \times {10^3}N$

$\therefore F = - 54\,kN$

This is the average force of resistance offered to the bullet.

**So the correct answer is option A.**

**Note:**If the time taken to penetrate the sheet before it comes to rest is given, then we can find the average resistive force as the ratio of change in momentum of the bullet to the time taken. Since distance travelled is given, we took the equation of motion involving distance to calculate the answer.

Recently Updated Pages

Why do we see inverted images in a spoon class 10 physics JEE_Main

A farsighted man who has lost his spectacles reads class 10 physics JEE_Main

State whether true or false The outermost layer of class 10 physics JEE_Main

Which is not the correct advantage of parallel combination class 10 physics JEE_Main

State two factors upon which the heat absorbed by a class 10 physics JEE_Main

What will be the halflife of a first order reaction class 12 chemistry JEE_Main

Other Pages

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

Electric field due to uniformly charged sphere class 12 physics JEE_Main

Which of the following distance time graph is representing class 11 physics JEE_Main

The resultant of vec A and vec B is perpendicular to class 11 physics JEE_Main

Choose the correct statements A A dimensionally correct class 11 physics JEE_Main

The figure below shows regular hexagons with charges class 12 physics JEE_Main