Question

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

• A. $26.8N$
• B. $50N$
• C. $15N$
• D. $30N$

Answer 1

The correct option is A $26.8N$

To find the tension in the string, moment about the contact point of the sphere and the plane should be zero.

Moment due to sphere about the contact point of the sphere and the plane

$M_{sp}=Wsin{30}^0\left(r\right)$; $r$ is the radius of the sphere.

Moment due to tension about the contact point of the sphere and the plane

$M_{AB}=T(r+\frac{rcos{30}^0}{2})$

Since, $M_{sp}=M_A$

$⟹T=\frac{100}{2+\sqrt{(}3)}$

$⟹T=26.81N$

Therefore, tension in the string is $26.81N$.