Question

Two shafts A and B are made of the same material. The diameter of shaft B is twice that of shaft A. The ratio of power which can be transmitted by shaft A to that of shaft B is (If maximum shear stress remains the same)

• A. $\frac{1}{2}$
• B. $\frac{1}{4}$
• C. $\frac{1}{8}$
• D. $\frac{1}{16}$

Answer 1

The correct option is C $\frac{1}{8}$

$P=T\omega$
Putting torsion formula
$\frac{T}{J}=\frac{\tau }{d/2}$
$\Rightarrow T=\frac{\tau \times \frac{\pi d^4}{32}}{d/2}=\frac{\tau \pi d^3}{16}$
Since material of both shafts are same, $\tau$ will be same
Now, if $P\propto d^3$
$d_B=2d_A$
$\frac{P_A}{P_B}=\frac{1}{8}$