Question 306: Work, Energy and Power & Circular Motion

Question

A particle is performing U.C.M. along the circumference of a circle of diameter 50 cm with frequency 2 Hz . The acceleration of the particle in $\mathrm{m} / \mathrm{s}^2$ is

Accepted Answer

Given, diameter of circle, $d=50 \mathrm{~cm}$
$$=50 	imes 10^{-2} \mathrm{~m}$$
and frequency, $f=2 \mathrm{~Hz}$
The acceleration of particle in a uniform circular motion can be given as
$$a=\omega^2 x$$
where, $\omega=$ angular frequency $=2 \pi f$
$$\begin{aligned}
\quad x & =	ext { distance from centre }=\frac{d}{2} \
\Rightarrow \quad a & =4 \pi^2 f^2 	imes \frac{d}{2}\quad	ext{... (i)}\end{aligned}$$
Substituting given values in Eq. (i), we get
$$a=4 \pi^2 	imes 4 	imes \frac{50 	imes 10^{-2}}{2}=4 \pi^2$$

Answer

$2 \pi^2$

Answer

$8 \pi^2$

Answer

$\pi^2$

Answer

$4 \pi^2$

Work, Energy and Power & Circular Motion

A particle is performing U.C.M. along the circumference of a circle of diameter 50 cm with frequency 2 Hz . The acceleration of the particle in \mathrm{m} / \mathrm{s}^2 is

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