An elastic string 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

Question

An elastic string 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 (A) 1/2 Ky2 (B) 1/2 Ky(2x + y) (C) 1/2 K(x2 + y2) (D) 1/2 K(x +y)2

Tardigrade Admin · Accepted Answer

In the string elastic force is conservative in nature.

∴ W = - Δ U

Work done by elastic force of string.

W = - (U_{F} - U_{i}) = U_{i} - U_{F}

W = \frac{1}{2} k x^{2} - \frac{k}{2} (x + y)^{2}

= \frac{1}{2} k x^{2} - \frac{1}{2} k (x^{2} + y^{2} + 2 x y)

= \frac{1}{2} k x^{2} - \frac{1}{2} k y^{2} - \frac{1}{2} k x^{2} - \frac{1}{2} k (2 x y)

= - k x y - \frac{1}{2} k y^{2}

Therefore, the work done against elastic force

W_{external} = - W = \frac{k y}{2} (2 x + y)

.

Q. An elastic string 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

$1/2 K y^{2}$

$1/2 Ky (2 x + y)$

$1/2 K (x^{2} + y^{2})$

$1/2 K (x + y)^{2}$

Q. An elastic string 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

1/2Ky2

1/2Ky(2x+y)

1/2K(x2+y2)

1/2K(x+y)2

Q. An elastic string 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

$1/2 K y^{2}$

$1/2 Ky (2 x + y)$

$1/2 K (x^{2} + y^{2})$

$1/2 K (x + y)^{2}$