Question

If a body moving in a circular path maintains constant speed of $10\text{m/s}$, then which of the following graphs correctly describes the relation between acceleration and radius?

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

The tangential acceleration of the particle is zero because it is moving with a constant speed.

The centripetal acceleration of the particle is $a_c=v^2/r,$ where $v=10\text{m/s}$ is the speed and $r$ is the radius.

Thus, acceleration of the particle is $a=\sqrt{a_t^2+a_c^2}=v^2/r$
So, $a\propto \frac{1}{r}$

Hence the graph between $a$ and $r$ will be a hyperbola.
Option C is the correct answer.