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Question

A spring gun of spring constant 90Ncm-1 is compressed 12cm by a ball of mass 16g. If the trigger is pulled, the velocity of the ball is


A

50ms-1

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B

9ms-1

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C

40ms-1

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D

60ms-1

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E

90ms-1

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Solution

The correct option is E

90ms-1


Step 1: Given data

Spring constant k=90Ncm-1

Compressed x=12cm

Mass of ball, m=16g

Step 2: Find the velocity of the ball

Let the velocity of the ball =v

Potential energy =U

Kinetic energy=K.E

The potential energy stored in the spring is,

U=(1/2)Kx2U=(1/2)×90×102×(0.12)2U=64.8J

The kinetic energy of the ball is,

K.E=(1/2)mv2K.E=(1/2)×16×10-3×v2

According to the law of conservation of energy,

The potential energy stored in the spring = kinetic energy of the ball

64.8=(1/2)×16×10-3×v2v2=8100v=90m/s

Hence, the velocity of the ball is 90m/s.

Hence, option E is correct.


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