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A spring of force constant k extends by ...

A spring of force constant k extends by a length X on loading . If T is the tension in the spring then the energy stored in the spring is

A

Statement-1 is true, Statement-2 is True, Statement -2 is a correct explanation for Statement-1.

B

Statement-1 is True, Statement-2 is True, Statement -2 is NOT a correct explanation for Statement-1.

C

Statement-1 is True, Statement-2 is False.

D

Statement - 1 is False, Statement -2 is True.

Text Solution

Verified by Experts

The correct Answer is:
D
Potential energy stored in the spring when it is extended by `x` is
`U_(1)=1/2 kx^(2)`
Potential energy stored in the spring when it is further extended by `x` is
`U_(2)=1/2 k (x+x)^(2)=2kx^(2)`
`:.` Work done `=` gain in potential energy `=U_(2)-U_(1)=2kx^(2)-1/2 kx^(2)=3/2 kx^(2)`
Hence (D) is correct.
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