Question

A sphere of weight W = 100 N is kept stationary on a rough inclined plane by a horizontal string AB as shown in the figure. Find the tension in the string and normal reaction on the sphere by the plane

Answer 1

from above diagram

$T\times R=f\times R$

$T=f.---1$

therefore

$Tcos\theta +f=mgsin\theta$

using the first equation

$T\times (1+cos\theta )=mgsin\theta$

since $\theta ={30}^0$

putting values will give

$T=\frac{100}{2+\surd 3}$

$f=T=26.8N$

and normal force = $mgsin\theta$

$=100\times \surd 32$

$N=50\sqrt{3}$