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Strength of Materials

Torsional Stresses

A solid circu...

Question

A solid circular shaft, ABC, has a total length of '3a'. A gear wheel positioned at B, at distance 'a' from the left hand end A, exerts a torque T. If the ends A and C are instantaneosuly locked in position by brakes just before the torque is applied, the torsional moments induced in both segments $T_{1} (A B) a n d T_{2} (B C)$ are in the ratio

A

3 : 1

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B

2 : 3

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C

1 : 2

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D

2 : 1

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Solution

The correct option is D 2 : 1
$T_{1} L_{A B}$ = $T_{2} L_{B C}$

$\frac{T_{1}}{T_{2}}$ = $\frac{L_{B C}}{L_{A B}}$ = $\frac{2}{1}$

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