Question

The earing of Miss Shon is $5cm$ long. She sits in a merry-go-round moving at 4 $m{s}^{-1}$ in a circle of radius $2m$. The time period of oscillations is nearly:

• A. $0.6s$
• B. $0.4s$
• C. $0.8s$
• D. None of these

Answer 1

The correct option is B $0.4s$

Time period of an object in a circular motion is given by $T=2\pi \sqrt{\frac{l}{\sqrt{g^2+{\left(\frac{v^2}{R}\right)}^2}}}$, So we have
$2\pi \sqrt{\frac{l}{\sqrt{g^2+{\left(\frac{v^2}{R}\right)}^2}}}=2\pi \sqrt{\frac{0.05}{\sqrt{(9.8{)}^2+{\left(\frac{(4{)}^2}{2}\right)}^2}}}=2\pi \sqrt{\frac{0.05}{\sqrt{(9.8{)}^2+{\left(\frac{(4{)}^2}{2}\right)}^2}}}=2\pi \sqrt{\frac{0.05}{12.65}}=0.395s\cong 0.4s$