Question

If work done in stretching a spring from xo to 2xo
is W, then work done in stretching this spring
from 2x, to 3x, will be :-
5W
(1) W
(2)5w
(3)3W/5
(4)5w/3​

Answer 1

Answer:

If work done in stretching a spring from xo to 2xo

is W, then work done in stretching this spring

from 2x, to 3x, will be

Answer 2

Answer:

The correct answer is $\frac{5w}{3}$ (Option 4).

Explanation:

The work done in stretching spring is done by the potential energy stored in the spring.

So we can say the change is potential energy while stretching a spring from one position to another is the work done in stretching the same.

The potential energy stored in the spring = $U= \frac{1}{2} kx^2$

From the position of $x_0$ to $2x_0$, change is potential energy or work done = $W= \frac{1}{2}k[ {(2x_0)}^2-(x_0)^2]= \frac{1}{2}k\times3x^2$

So, from this we can say that:-

$\frac{W}{3} =\frac{1}{2}kx^2$

Now according to the question work done while stretching the spring from $2x_0$ to $3x_0$ is:-

$W= \frac{1}{2}k[ {(3x_0)}^2-(2x_0)^2]= 5\times \frac{1}{2}kx^2= \frac{5W}{3}$

Therefore the work done is $\frac{5w}{3}$.