Question

If the maximum shear stress is limited to 75N/mm${}^2$ then the radius ( in mm) of solid shaft for 7.5 kW motor operating at 30 Hz is

• A. 6.96 mm
• B. 13.94 mm
• C. 27.8 mm
• D. 7.2 mm

Answer 1

The correct option is A 6.96 mm

Power , $P=T\cdot \omega$

$=T\times \left(2\pi f\right)$

$\Rightarrow 7.5\times {10}^3=T\times 2\pi \times 30$

$\Rightarrow T=39.79Nm$

$\frac{T}{J}=\frac{\tau }{r}=\frac{39.79\times {10}^3}{75}=\frac{\pi d^4}{32\left(\frac{d}{2}\right)}$
$\Rightarrow d=13.93mm$

$\therefore r=6.97mm$