Question

A bob of mass $500\text{g}$ attached to a light inextensible string revolving vertically in a radius $R$ is given an initial velocity $v=\sqrt{7gR}$ at the bottom most point. The tension in the string at the bottom most point is

• A. $40\text{N}$
• B. $35\text{N}$
• C. $5\text{N}$
• D. $20\text{N}$

Answer 1

The correct option is A $40\text{N}$

At the bottom most point, let the tension be $\text{T}$ is upwards & weight of bob is downwards


$\therefore$ By the FBD of the bob at the bottom most point, we get

$T-mg=\frac{m{v}^2}{R}$
$\Rightarrow T=mg+\frac{m{v}^2}{R}$

$=mg+\frac{m(\sqrt{7gR}{)}^2}{R}=8mg$

Where the mass $m$ of the bob is given as $500\text{g}=0.5\text{kg}$

$\Rightarrow T=8\times 0.5\times 10=40\text{N}$

Hence option A is the correct answer