Question

A particle performing U.C.M with radius 3 m and liner speed 3 m/s. if $\stackrel{-}{r}$ is a radius vector its centripetal acceleration $\stackrel{-}{a}$ is

• A. $\stackrel{-}{a}=-9\stackrel{-}{r}$
• B. $\stackrel{-}{a}=-27\stackrel{-}{r}$
• C. $\stackrel{-}{a}=27\stackrel{-}{r}$
• D. $\stackrel{-}{a}=-3\stackrel{-}{r}$

Answer 1

Answer: (D)

$\stackrel{-}{a}=-3\stackrel{-}{r}$

$\text{Given, there is a particle which undergoes uniform circular motion.}$

$\begin{array}{c}r=3m\\ \text{and, speed}=3m/s\text{.}\end{array}$

$\begin{array}{c}\text{We know, particles undergo circular}\\ \text{motion due to a force directed}\\ \text{towards the centre,}{F}_{centripetal}.\\ \text{Thus, direction of centripetal acceleration}\left(\overrightarrow{a}\right)\text{must be}\\ \text{opposite of}\overrightarrow{r}\text{.}\end{array}$

$\begin{array}{c}\text{we know,}|\overrightarrow{a}|=\frac{|\overrightarrow{v}{|}^2}{r}=\frac{3\times 3}{3}m/s^2=3m/s^2\text{.}\\ \text{Hence,}\overrightarrow{a}=-\overrightarrow{3r}\end{array}$