Question

Two particles $p$ and $q$ are located at distances $r_p$ and $r_q$ respectively from the centre of a rotating disc such that $r_p$ >$r_q$. Then:

• A. both $p$ and $q$ have the same centripetal acceleration
• B. both $p$ and $q$ do not have any acceleration
• C. $p$ has greater centripetal acceleration than $q$
• D. $q$ has greater centripetal acceleration than $p$

Answer 1

The correct option is C $p$ has greater centripetal acceleration than $q$

When a particle rotates in a circle, its centripetal acceleration is given by $\frac{v^2}{r}$ where $r$ is the radial position of the particle and $v$ is its linear velocity at that instant.

Now $v$ = $\frac{2\pi r}{t}$ so its centripetal acceleration can also be represented by the formula $\frac{4{\pi }^{2}r}{t^2}$.

Since $t$ is the same for both the particles (as they are on the same disc) the particle which is at a greater distance from the centre has greater acceleration.