# If a shaft is required to transmit twice the power at twice the speed for which it is designed, its diameter must

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If a shaft is required to transmit twice the power at twice the speed for which it is designed, its diameter must
1. increase two times
2. reduce two times
3. remain same
4. increase three times

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Correct Answer - Option 3 : remain same

Concept:

The power transmitting capacity of the shaft is given by

$P = \frac{{2\pi NT}}{{60}}$

P ∝ NT

Torsion equation:

$\frac{T}{J} = \frac{{{\tau _{max}}}}{R} = \frac{{G\theta }}{l}$

$T = {\tau _{max}} \times \frac{J}{R}$

$J = \frac{\pi }{{32}} \times {D^4}$

$T = \frac{{{\tau _{max}}\; \times \;\pi \; \times {D^3}\;}}{{16}}$

T ∝ D3

P ∝ NT

P ∝ ND3

Calculation:

Given:

P2 = 2P1, N2 = 2N1

$\frac{P_2}{P_1}=\frac{N_2}{N_1}\times\frac{D_2^3}{D_1^3}$

$\frac{2P_1}{P_1}=\frac{2N_1}{N_1}\times\frac{D_2^3}{D_1^3}$

D1 = D2