Question

The figure shows the total acceleration $a=32m{s}^{-2}$ of a moving particle moving clockwise in a circle of radius $R=1\text{m}\text{.}$ What are the centripetal acceleration $a$ and speed of the particle at the given instant?

• A. $16\sqrt{3}m{s}^{-2},4\sqrt{3}m{s}^{-1}$
• B. $16\sqrt{3}m{s}^{-2},4m{s}^{-1}$
• C. $16m{s}^{-2},16m{s}^{-1}$
• D. $16m{s}^{-2},4m{s}^{-1}$

Answer 1

Answer: (D)

Given,
Total acceleration, $a=32m{s}^{-2}$

$\therefore$ Centripetal acceleration, $a_c=32cos60^{\circ }$
$=32\times \frac{1}{2}$
$=16m{s}^{-2}$
Also, we know that, $a_c=\frac{v^2}{R}=16m{s}^{-2}$
$\Rightarrow \frac{v^2}{1}=16$ $\left[\because R=1\right]$
$\Rightarrow v^2=16{\text{m}}^{\text{2}}{\text{ s}}^{\text{-2}}$
$\therefore$ Speed of the particle $v=4m{s}^{-1}$