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Question

A ball of mass 2Kg moving with velocity 3ms-1, collides with spring of natural length 2m and force constant 144Nm-1. What will be the length of the compressed spring?


A

2m

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B

1.5m

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C

1m

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D

0.5m

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Solution

The correct option is B

1.5m


Step 1: Given data

Mass of a ball m=2Kg

Velocity of a ball v=3ms-1

Natural length of a spring =2m

Force constant of a spring, k=144Nm-1

Let the displacement of spring be=Xmeter

Step 2: Calculating the length of compresses spring

Here, when ball collides with the spring, the kinetic energy of a ball will get converted into the potential energy of spring, that is

12mv2=12kX2mv2=kX22×32=144×X218=144×X2X=122m

Now the length of compressed spring is given by:

Compressed length=naturallength-X

=2-122=42-122=1.5m

Hence, option(B) is the correct answer.


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