Question

A particle is suspended from a fixed point by a string of length $10\text{m}$. The particle is given a horizontal velocity at the lowest point. The string slacks after the particle have reached a height of $16\text{m}$ above the lowest point. What is the velocity of the particle just before the string slacks?

• A. $3\sqrt{15}\text{m/s}$
• B. $2\sqrt{15}\text{m/s}$
• C. $4\sqrt{15}\text{m/s}$
• D. $5\sqrt{15}\text{m/s}$

Answer 1

The correct option is B $2\sqrt{15}\text{m/s}$


$\text{cos}\theta =\frac{6}{10}=\frac{3}{5}$
String slacks when Tension $T=0$
At point $P$,
$T=0$
$\Rightarrow \frac{m{v}^2}{R}=\text{mg cos}\theta$
$\Rightarrow \frac{v^2}{R}=\text{g cos}\theta$
$\Rightarrow v=\sqrt{\text{R g cos}\theta }$
$\Rightarrow v=\sqrt{10\times 10\times \frac{3}{5}}$
$v=2\sqrt{15}\text{m/s}$
Hence, option $\left(b\right)$ is correct.