Question

The work done in extending a spring by l is w.The work done in further extenstion l will be
(1) 3w
(2) 2w
(3) w/2
(4) w/4​

Answer 1

Answer:

Option (1) 3W

Explanation:

The work done in a spring is stored as potential energy

The potential energy of a spring is given by 1/2kx^2 where k is the spring constant and x is the compression or extension in the spring

Here the spring is extended by l

Therefore, the work done

$W=\frac{1}{2}kl^2$

When the spring is extended further by l, total extension will be 2l

Therefore, the work done

$W'=\frac{1}{2}k(2l)^2=\frac{1}{2}k\times 4l^2=4W$

Extra work done = W' - W = 4W - W = 3W

Therefore, the work done in further extension of the spring will be 3w

Answer 2

Answer:

initial work done by spring=1/2kx^2=w

final work done by spring=1/2k(2x)^2=1/2k×4x^2=4w

total work done=final work done - initial work done

=4w-w=3w