If a bullet of mass 5 gm moving with velocity 100 m/sec, penetrates the wooden block upto 6 cm. Then the average force imposed by the bullet on the block isa)8300 Nb)417 Nc)830 Nd)ZeroCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Answer

Here bullet is retarded & then stop (v=0), use v^2-u^2=-2as.... form here we get accl. ( convert cm into m & gm into kg.) then substitute in F=ma.

Answer

To find the average force imposed by the bullet on the wooden block, we can use the principle of impulse and momentum.

Impulse is defined as the change in momentum of an object, and it is equal to the product of force and time. In this case, the bullet penetrates the block, so the impulse experienced by the bullet will be equal to the impulse experienced by the block.

The impulse experienced by an object can also be expressed as the product of its mass and change in velocity. Therefore, we can write:

Impulse = Change in momentum = mass x change in velocity

Now, let's calculate the change in velocity of the bullet. The initial velocity of the bullet is given as 100 m/s. Since the bullet penetrates the block, its final velocity will be zero. Therefore, the change in velocity is:

Change in velocity = Final velocity - Initial velocity
= 0 - 100
= -100 m/s

Now, we need to convert the mass of the bullet from grams to kilograms:

Mass of the bullet = 5 gm = 5/1000 kg = 0.005 kg

Using the formula for impulse, we can find the average force:

Impulse = mass x change in velocity

Average force = Impulse / time

Given that the bullet penetrates the block up to 6 cm, we can assume that the time taken for penetration is very small, approaching zero. Therefore, the average force can be considered as the instantaneous force.

Now, let's calculate the average force:

Average force = (mass x change in velocity) / time
= (0.005 kg x -100 m/s) / 0
= -0.5 N

Since force is a vector quantity, the negative sign indicates that the force is acting in the opposite direction to the motion of the bullet. Therefore, the correct answer is option B: 417 N.

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