Question

A body is rotated in a horizontal circle of radius $7m$ with an uniform speed. The period of rotation for which the acceleration is equal to 3 times of acceleration due to gravity.

• A. $2.61s$
• B. $2.87s$
• C. $3.31s$
• D. $3.07s$

Answer 1

The correct option is D $3.07s$

Centripetal acceleration $a_r=r{\omega }^2$
$\because \omega =\frac{2\pi }{T}$
$a_r=r{\left(\frac{2\pi }{T}\right)}^2=r\frac{4{\pi }^2}{T^2}$

Given $a_r=3\times g$
$\Rightarrow 3g=\frac{4{\pi }^{2}r}{T^2}$
$\Rightarrow T^2=\frac{4{\pi }^{2}r}{3g}=\frac{4\times {\pi }^2\times 7}{3\times 9.8}=9.39$
$\Rightarrow T=3.07s$