Question

A circular platform rotates around a vertical axis with angular velocity $\omega =10rad/s$. On the platform is a ball of mass 1 kg, attached to the long axis of the platform by a thin road of length 10 cm ($\alpha ={30}^0$). Find normal force exerted by the ball on the platform (in newton). Friction is absent.

Answer 1

Given,

Mass,$M=1kg$

Angular velocity, $\varpi =10rad/s$

Length of rod, $r=0.1m$

Angle, $\alpha ={30}^o$

From the figure,

Horizontal Equilibrium forces.

$T\cos {30}^o=m{\varpi }^{2}r=1\times {10}^2\times 0.1=10$

$T=\frac{10}{\cos {30}^o}=\frac{20}{\sqrt{3}}\dots \dots \left(1\right)$

Vertical forces in equilibrium.

$N=mg-T\sin {30}^o=1\times 10-\frac{20}{\sqrt{3}}\times \frac{1}{2}=4.22N$

Hence, normal reaction on ball is $4.22N$