Question

A $500g$ particle tied to one end of a string is whirled in a vertical circle of circumference $14m$.If the tension at the highest point of its path is $2N$, what is its speed? (in m/s)

• A. $4.365$
• B. $5.369$
• C. $5.546$
• D. $4.331$

Answer 1

The correct option is C $5.546$

as the diagram shows

balancing the force at point $P$

given that $T=2N$, $m=0.5kg$ and $R=\frac{14}{2\pi }=2.23m$

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

$\Rightarrow v=\sqrt{R\frac{(T+mg)}{m}}$

$\Rightarrow v=\sqrt{2.23\times \frac{(2+0.5\times 10)}{0.5}}=5.546m/s$