Question

Figure shows a rod of length 20 cm pivoted near an end and which is made to rotate in a horizontal plane with a constant angular speed. A ball of mass m is suspended by a string also of length 20 cm from the other end of the rod. If the angle $\theta$ made by the string with the vertical is $30,$ find the angular speed of the rotation.
Take $g=10m/s^2.$

• A. $\omega =8radians/sec$
• B. $\omega =4.4radians/sec$
• C. $\omega =14.4radians/sec$
• D. $\omega =44.4radians/sec$

Answer 1

The correct option is B $\omega =4.4radians/sec$

$Tcos30=mgTsin30=m{\omega }^2(l+lsin\theta )tan30=\frac{{\omega }^{2}l(1+sin30)}{g}{\omega }^2=\frac{\frac{1}{\sqrt{3}}\left(10\right)}{0.2\left(\frac{3}{2}\right)}\omega =4.4radians/sec$