A uniform wire of length L and radius r is twisted by an angle α. If modulus of rigidity of the wire is η, then the elastic potential energy stored in wire, is

Question

A uniform wire of length L and radius r is twisted by an angle α. If modulus of rigidity of the wire is η, then the elastic potential energy stored in wire, is (A) (π η r4 α/2 L2) (B) (π η r4 α2/4 L) (C) (π η r4 α/4 L2) (D) (π η r4 α2/2 L)

Tardigrade Admin · Accepted Answer

U= work done We know Work done =(π S r4 φ2/4 L) Where, φ= Angle of twist =α S= Modulus of rigidity =4 Substituting values U=(π η r4 α2/4 L)

Q. A uniform wire of length $L$ and radius $r$ is twisted by an angle $α$ . If modulus of rigidity of the wire is $η$ , then the elastic potential energy stored in wire, is

$\frac{π η r ^{4} α}{2 L ^{2}}$

$\frac{π η r ^{4} α ^{2}}{4 L}$

$\frac{π η r ^{4} α}{4 L ^{2}}$

$\frac{π η r ^{4} α ^{2}}{2 L}$

$U =$ work done
We know
Work done $= \frac{π S r ^{4} ϕ ^{2}}{4 L}$
Where,
$ϕ =$ Angle of twist $= α$
$S =$ Modulus of rigidity $= 4$
Substituting values
$U = \frac{π η r ^{4} α ^{2}}{4 L}$

Q. A uniform wire of length L and radius r is twisted by an angle α. If modulus of rigidity of the wire is η, then the elastic potential energy stored in wire, is

2L2πηr4α​

4Lπηr4α2​

4L2πηr4α​

2Lπηr4α2​