Question

The arms of Porter governor are each 25 cm long and pivoted on the governor axis. Mass of each ball is 5 kg and mass of central sleeve is 30 kg. The radius of rotation is 15 cm. When the sleeve begins to rise and reaches to 20 cm at the maximum speed, The range of speed is.

• A. 176.9 rpm
• B. 204.3 rpm
• C. 27.3 rpm
• D. 214.3 rpm

Answer 1

The correct option is C 27.3 rpm

$h=\frac{g}{m{\omega }^2}(m+\frac{M(1+k)}{2})$

k = 1 for equal arms, $g=981cm/s^2$

$=\frac{g}{m{\omega }^2}(m+M)$

$=\frac{g}{{\omega }^2}\left(\frac{35}{5}\right)$

$h=\frac{7g}{{\omega }^2}$

$\sqrt{(25{)}^2-{15}^2}=\frac{7g}{{\omega }_2^2}$

${\omega }^2=21.4rad/s$

$N_2=204.42rpm$

$N_2-N_1=27.42rpm$