Question

A particle is revolving in a circular path of radius $200m$ at a speed of $20m/s$. Its speed is increasing at the rate of $\sqrt{5}m/s^2$. Its acceleration is

• A. $2m/s^2$
• B. $\sqrt{7}m/s^2$
• C. $3m/s^2$
• D. $\sqrt{5}m/s^2$

Answer 1

The correct option is C $3m/s^2$

As particle is moving along a circular path, it will experience two types of acceleration:

$1)$ Tangential acceleration:

This is the acceleration that occurs in straight line, whose value is given to us as $\sqrt{5}m/s^2$

$2)$ Centripetal acceleration $=\frac{v^2}{r}=\frac{20\times 20}{200}=2m/s$

so, total acceleration =$\sqrt{(\sqrt{5}{)}^2+2^2}=3m{s}^{-2}$