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

Question

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 (A) (k y/2)(x+2 y) (B) (k/2)(2 x+y) (C) k y(x+2 y) (D) (k y/2)(2 x+y)

Tardigrade Admin · Accepted Answer

According to the question
In the first condition,

W_{1} = \frac{1}{2} k x^{2} ... (i)

In the second condition

W_{2} = \frac{1}{2} k (x + y)^{2} ... (ii)

Work for

x

to

y

expansion

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

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

= \frac{1}{2} k [y^{2} + 2 x y]

= \frac{1}{2} k y [y + 2 x]

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

$\frac{k y}{2} (x + 2 y)$

$\frac{k}{2} (2 x + y)$

$k y (x + 2 y)$

$\frac{k y}{2} (2 x + y)$

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

2ky​(x+2y)

2k​(2x+y)

ky(x+2y)

2ky​(2x+y)

According to the question In the first condition, W1​=21​kx2...(i) In the second condition W2​=21​k(x+y)2...(ii) Work for x to y expansion =21​k(x+y)2−21​kx2 =21​k[x2+y2+2xy−x2] =21​k[y2+2xy] =21​ky[y+2x]

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

$\frac{k y}{2} (x + 2 y)$

$\frac{k}{2} (2 x + y)$

$k y (x + 2 y)$

$\frac{k y}{2} (2 x + y)$