JEE Problem

Classical Mechanics Level 3

A bullet loses $\dfrac{1}{n}$ of its velocity passing through a wooden block. The number of such blocks that are required to stop the bullet is

Clarifications : The bullet loses energy when passing through the first block. Each subsequent block requires the same amount of energy to pass through.

None of these choices

\dfrac{n^2}{2n-1}

Infinite

\dfrac{2n^2}{n-1}

n

1 solution

Manisha Garg
Dec 18, 2015

The energy loss is:

ΔE=1/2×mv²−1/2×m(v−v/n)².

Hence, the number of planks x becomes:

x = 1/2×mv² ÷ ΔE = n²/2n−1.

You are assuming a constant ΔE, but what is constant is the relative energy loss at each step not the absolute amount of energy loss. Just work any numerical case and you will see that the correct answer is infinite.

Oscar Rojas - 5 years, 5 months ago

Infinite is a good choice for such answers. THe Velocity never reduces to zero.

Aditya Narayan Sharma - 5 years, 4 months ago

I think infinite, Its a kind of paradox, but i also found the correct answer, So i ticked the more mathematical one :P. But Infinite was a correct choice,like a ball say bounces 1/2 the height after collision with the floor, So

1st h, then h/2,..

h,h/2,h/4,.....

This forms an infinite GP.

Thats an paradox, the ball bounces infinitely,And covers a total distance 2h by infinite GP Sum ...

Isnt it @Aditya Narayan Sharma ?

Md Zuhair - 3 years, 11 months ago

What is the correct answer? I also chose infinite. I have the same doubt as @Aditya Narayan Sharma .

@Md Zuhair , @Aryan Sanghi

Vinayak Srivastava - 2 months, 2 weeks ago

Ya, the answer is wrong. It should be infinite. The relative energy loss is to be considered, not absolute energy loss.

Aryan Sanghi - 2 months, 2 weeks ago

Ok, let me report it. Thanks for your help! :)

Vinayak Srivastava - 2 months, 2 weeks ago

Can you please tell how to solve this problem?

Vinayak Srivastava - 2 months, 2 weeks ago

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