Question

Figure shows the total acceleration $a=32m/s^2$ of a moving particle moving clockwise in a circle of radius $R=1m$. What are the centripetal acceleration $a$ and speed $v$ of the particle at given instant?

• A. $16\sqrt{3}m/s^2,4\sqrt{3}m/s$
• B. $16\sqrt{3}m/s^2,4m/s$
• C. $16m/s^2,16m/s$
• D. $16m/s^2,4m/s$

Answer 1

The correct option is D $16m/s^2,4m/s$

Given,
Total acceleration, $a=32m/s^2$

$\therefore$ Centripetal acceleration, $a_c=32\cos {60}^{\circ }$
$=32\times \frac{1}{2}$
$=16m/s^2$

Also, we know that, $a_c=\frac{v^2}{R}=16m/s^2$
$\Rightarrow \frac{v^2}{1}=16[\because R=1]$

$\Rightarrow v^2=16m/s^2$

$\therefore$ Speed of the particle $v=4m/s$