Question

The figure shows the total acceleration $a=32\,ms^{- 2}$ 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. $16\sqrt{3}\,ms^{- 2}, \, 4\sqrt{3}\,ms^{- 1}$
• B. $16\sqrt{3}\,ms^{- 2}, \, 4\,ms^{- 1}$
• C. $16\,ms^{- 2}, \, 16\,ms^{- 1}$
• D. $16\,ms^{- 2}, \, 4\,ms^{- 1}$

Answer 1

Answer: (D)

Given,
Total acceleration, $a=32\,ms^{- 2}$

$\therefore \, \, $ Centripetal acceleration, $a_{c}=32cos 60^\circ $
$=32\times \frac{1}{2}$
$=16\,ms^{- 2}$
Also, we know that, $a_{c}=\frac{v^{2}}{R}=16\,ms^{- 2}$
$\Rightarrow \, \, \, \frac{v^{2}}{1}=16$ $\left[\because \, \, R = 1\right]$
$\Rightarrow v^{2}=16\,\text{m}^{\text{2}}\text{ s}^{\text{-2}}$
$\therefore \, \, $ Speed of the particle $v=4\,ms^{- 1}$