You visited us 1 times! Enjoying our articles? Unlock Full Access!

Work Done, Varying Force and Path

A spring whic...

Question

A spring which is initially in its unstretched condition, is first stretched by a length x and then again by a further length x. The work done in the first case is $W_{1}$ and in the second case is $W_{2}$ . Then:

W_{2} = W_{1}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

W_{2} = 2 W_{1}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

W_{2} = 3 W_{1}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

W_{2} = 4 W_{1}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $W_{2} = 3 W_{1}$
We know that,
The work done in stretching the spring by a length x-
$W_{1} = \frac{1}{2} k x^{2} . . . (1)$
And the work done in again stretching the spring by a further length x
$W_{2} = \frac{1}{2} k (2 x)^{2} - \frac{1}{2} k x^{2}$
$W_{2} = \frac{1}{2} k \times 4 x^{2} - \frac{1}{2} k x^{2}$
$W_{2} = 3 \times \frac{1}{2} k x^{2} . . . (2)$
From equations (1) and (2),
$W_{2} = 3 W_{1}$ .

Suggest Corrections

Similar questions

A spring, which is initially in its unstretched condition, is first stretched by a length $x$ and then again by a further length $x$ . The work is done in the first case $W_{1}$ and in the second case $W_{2}$ . Find $\frac{W_{2}}{W_{1}}$ .

Q. A spring of unstretched length

l

and force constant

k

is stretched by a small length

x

. It is further stretched by another small length

y

. The work done in the second stretching is

Q. An elastic spring of unstretched length

L

and force constant

K

is stretched by a small length

x

. It is further stretched by another small length

y

. Work done during the second stretching is

Q. An elastic spring of unstretched length

L

and force constant

K

, is stretched by a small length

x

. It is further stretched by another small length

y

. calculate the work done during the second stretching is:

Q. An elastic string of unstretched length

^{'} L^{'}

and force constant

^{'} k^{'}

is stretched by a small length

^{'} x^{'}

. It is further stretched by small length

^{'} y^{'}

. The work done in the second stretching is

Join BYJU'S Learning Program

A spring which is initially in its unstretched condition, is first stretched by a length x and then again by a further length x. The work done in the first case is W1 and in the second case is W2. Then:

The correct option is C W2=3W1We know that, The work done in stretching the spring by a length x- W1=12kx2...(1) And the work done in again stretching the spring by a further length x W2=12k(2x)2−12kx2 W2=12k×4x2−12kx2 W2=3×12kx2...(2) From equations (1) and (2), W2=3W1.

A spring which is initially in its unstretched condition, is first stretched by a length x and then again by a further length x. The work done in the first case is $W_{1}$ and in the second case is $W_{2}$ . Then: