Question

A particle is moving along a circular path with a constant speed $30m/s$. What is change in velocity of particle, when it decreases an angle of ${90}^{\circ }$ at the center of the circle ?

• A. Zero
• B. $30\sqrt{2}m{s}^{-1}$
• C. $60\sqrt{2}m{s}^{-1}$
• D. $\frac{30}{\sqrt{2}}m{s}^{-1}$

Answer 1

Answer: (B)

$30\sqrt{2}m{s}^{-1}$

Since the angle decreases by ${90}^{\circ }$. if the initial velocity is in a downward direction, then the final velocity will be in right direction.

The change in velocity for the body in circular path will be:

$\Delta v=v_f-v_i$
$=30\hat{i}-30\hat{j}$

$\left|\Delta v\right|=\sqrt{{30}^2+{\left(-30\right)}^2}$

$=30\sqrt{2}m{s}^{-1}$