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Question

A 16kg block moving on a frictionless horizontal surface with a velocity of 4ms-1compresses an ideal spring and comes to rest. If the force constant of the spring be 100Nm-1, then the spring is compressed by


A

1.6m

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B

4m

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C

6.1m

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D

3.2m

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Solution

The correct option is A

1.6m


Step 1: Given data

Mass of the block, m=16kg

Velocity of the block, v=4m/s

Spring constant, k=100N/m

Step 2. Find the compression in spring, x

Kinetic energy is half of the product of the mass and the square of the velocity.

Potential energy of the spring is equal to half of the product of the spring constant and the square of the compression in the spring.

Applying conservation of energy, kinetic energy, K.E. is equal to the potential energy of the spring, P.E.

K.E.=P.E.

12mv2=12kx2

16×4×42=100×x22

100×x2=16×4×4

x2=16×4×4100

x=1.6m

Hence, option (A) is correct.


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