Question

A sphere is suspended by a thread of length $l$ . What minimum horizontal velocity has to be imparted the ball for it to reach the height of the suspension?

• A. $gl$
• B. $2gl$
• C. $\sqrt{gl}$
• D. $\sqrt{2gl}$

Answer 1

Answer: (D)

$\sqrt{2gl}$

Let the initial velocity given to the sphere be $u$. At the height of suspension i.e point B, its velocity becomes zero i.e $v=0$

Work-energy theorem : $W_{allforces}=\Delta K.E$

$\therefore$ $-mgl=\frac{1}{2}m{v}^2-\frac{1}{2}m{u}^2$

$-mgl=0-\frac{1}{2}m{u}^2$ $⟹mgl=\frac{1}{2}m{u}^2$

$\therefore$ $u=\sqrt{2gl}$