Question

A uniform rod hinged at its one end is allowed to rotate in the vertical plane. Rod is given an angular velocity $\omega$ in its vertical position as shown in figure. The value of $\omega$ for which the force exerted by the hinge on rod is zero in this position is

• A. $\sqrt{\frac{g}{L}}$
• B. $\sqrt{\frac{2g}{L}}$
• C. $\sqrt{\frac{g}{2L}}$
• D. $\sqrt{\frac{3g}{L}}$

Answer 1

The correct option is B $\sqrt{\frac{2g}{L}}$

Force exerted by the centrifugal is equal to weight to cancel the reaction force exerted by hinge.

$\Rightarrow m{\omega }^{2}r=mg$....eq(1)

where $r=\frac{L}{2}$

by eq(1) we obtain

$\Rightarrow w=\sqrt{\frac{g}{r}}=\sqrt{\frac{2g}{L}}$

Hence option B is correct .