A long spring, when stretched by a distance x, has potential energy U. On increasing the stretching to nx, the potential energy of the spring will be

Question

A long spring, when stretched by a distance x, has potential energy U. On increasing the stretching to nx, the potential energy of the spring will be (A)  (U/n)  (B)  nU  (C)  n2U  (D)  (U/n2)

Tardigrade Admin · Accepted Answer

Potential energy of the spring U=(1/2)kx2 ...(i) and U'=(1/2)k(nx)2 ⇒ U'=n2(1/2)k x ∴ U'=n2U [From Eq. (i)]

Q. A long spring, when stretched by a distance $x,$ has potential energy $U$ . On increasing the stretching to $n x,$ the potential energy of the spring will be

$\frac{U}{n}$

$n U$

$n^{2} U$

$\frac{U}{n ^{2}}$

Potential energy of the spring
$U = \frac{1}{2} k x^{2}$ ...(i)
and $U^{'} = \frac{1}{2} k (n x)^{2}$
$\Rightarrow$ $U^{'} = n^{2} \frac{1}{2} k x$
$∴$ $U^{'} = n^{2} U$ [From Eq. (i)]

Q. A long spring, when stretched by a distance x, has potential energy U. On increasing the stretching to nx, the potential energy of the spring will be

nU​

nU

n2U

n2U​