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Question

A dart is loaded into a spring-loaded toy dart gun by compressing the spring by a distance of d. For the next loading, the spring is compressed by a distance 2d. How much faster does the second dart leave the gun compared to first?

A
Four times
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B
Two times
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C
Half times
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D
One-fourth times
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Solution

The correct option is B Two times
The energy stored in the dart due to the compression of spring gets converted into kinetic energy. If m is the mass of the dart, then12kd2=12mv2o (where vo is the velocity in first case and k is spring constant)12k(2d)2=12mv2 (where v is the velocity in second case) 14=v2o v2v=2vo

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