Question

A metallic bob of mass ‘$m$’ attached to a string, is raised through a height of $50\text{cm}$ and released. At what distance along the vertical from the point of suspension should a nail be placed so that the bob just completes a circle with the nail as the centre?

• A. $0.2\text{m}$
• B. $2\text{m}$
• C. $1\text{m}$
• D. $1.8\text{m}$

Answer 1

The correct option is D $1.8\text{m}$


The bob is raised through a height of $50\text{cm}$.
Velocity of the bob as it comes to the mean position $v=\sqrt{2gh}=\sqrt{2\times 10\times 0.5}$
$\Rightarrow v=\sqrt{10}\text{m/s}$

Velocity at mean position required to just complete a circle around the nail $=\sqrt{5gr}$
where $r$ is the radius of the circle with the nail as the centre.

$\therefore v=\sqrt{10}=\sqrt{5gr}$
$\Rightarrow r=\frac{10}{5g}=\frac{2}{10}$
$\Rightarrow r=0.2\text{m}$
$\therefore$ The radius of the circle is $0.2\text{m}$.
Distance from the point of suspension of pendulum $x=2-0.2=1.8\text{m}$