A long spring, when stretched by a distance x, has potential energy U. On increasing the stretching to rue, 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 rue, 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)k x2 ?(i) and U=(1/2)k(nx)2 ⇒ U=n2(1/2)k x2 ∴ U=n2U [From Eq. (i)]

Q. A long spring, when stretched by a distance x, has potential energy U. On increasing the stretching to rue, 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 $U = \frac{1}{2} k (n x)^{2}$ $\Rightarrow$ $U = n^{2} \frac{1}{2} k x^{2}$ $∴$ $U = n^{2} U$ [From Eq. (i)]