A cylindrical rod of diameter 10 {mm} and length 1.0 {m} is fixed at one end. The other end is twisted by an angle of 10^{\circ} by applying a torque. If the maximum shear strain in the rod is {p} \times 10^{-3}, then p is equal to ____________(round off to two decimal places).

GATE Mechanical Engineering (ME) 2019 Shift 1 Solved Paper

Question : 24 of 65

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A cylindrical rod of diameter

10 {mm}

and length

1.0 {m}

is fixed at one end. The other end is twisted by an angle of

10^{∘}

by applying a torque. If the maximum shear strain in the rod is

{p} ×

10^{-3}

, then

p

is equal to ____________(round off to two decimal places).

Solution:

From the torsion equation,

\;{T_{m a x}}/{R}=\;{G θ}/{L}

Maximum shear strain

=\;{τ_{mas}}/{G}=\;{R θ}/{L}=\;{5 × 10 × {π}/{10}}/{1000}=0.87 × 10^{-3}

On comparing with

{p} × 10^{-3}

, we have

{p}=0.87

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