Question

Two shaft of different diameter d₁ and d₂ are made from same material and are of same length under the action of same torque T the ratio of strain energy V₁/V₂
1. [d₂/d₁]³
2. [d₁/d₂]²
3. [d₂/d₁]²
4. [d₂/d₁]⁴

Answer 1

Correct Answer - Option 4 : [d₂/d₁]⁴

Concept:

The strain energy of shaft due to torque T,

\({U} = \frac{{{T^2}l}}{{2G\frac{\pi }{{32}}{{\left( {d} \right)}^4}\;}}\)

Where,

d = diameter of the shaft

T = Applied torque

l = length of the shaft

G = modulus of rigidity

Calculation:

Given;

d₁ = diameter of first shaft

d₂ = diameter of the second shaft

T = applied torque

The strain energy of 1st shaft is

\({V_1} = \frac{{{T^2}l}}{{2G\frac{\pi }{{32}}{{\left( {d_1} \right)}^4}\;}}\)

The strain energy of 2nd shaft is

\({V_2} = \frac{{{T^2}l}}{{2G\frac{\pi }{{32}}{(d_2)^4}\;}}\)

So,

\(\frac{{{V_1}}}{{{V_2}}} = {\left( {\frac{{{d_2}}}{{{d_1}}}} \right)^4}\)