PYQ NEET- Motion In A Plane L-5

Question: A particle moves in a circle of radius $5 \mathrm{~cm}$ with constant speed and time period $0.2 \pi \mathrm{s}$. The acceleration of the particle is#

A) $25 \mathrm{~m} / \mathrm{s}^2$

B) $36 \mathrm{~m} / \mathrm{s}^2$

C) $5 \mathrm{~m} / \mathrm{s}^2$

D) $15 \mathrm{~m} / \mathrm{s}^2$

Answer: $5 \mathrm{~m} / \mathrm{s}^2$#

Sol:#

Given, $r=5 \mathrm{~cm}=5 \times 10^{-2} \mathrm{~m}$ $T=0.2 \pi \mathrm{s}$

We know that acceleration is given by

$$ \begin{aligned} a & =r \omega^2=\frac{4 \pi^2}{T^2} r=\frac{4 \times \pi^2 \times 5 \times 10^{-2}}{(0.2 \pi)^2} \ & =5 \mathrm{~m} / \mathrm{s}^2 \end{aligned} $$