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 and speed $v$ of the particle at given instant?

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

Answer 1

Answer: (B)

$16m/s^2, 4m/s$

Answer 2

Given,
Total acceleration, $a=32\, m / s ^{2}$
$\therefore$ Centripetal acceleration, $a_{c} =32 \cos 60^{\circ}$
$=32 \times \frac{1}{2}$
$=16 m / s ^{2}$
Also, we know that, $a_{c}=\frac{V^{2}}{R}=16\, m / s ^{2}$
$\Rightarrow \frac{V^{2}}{1} =16 [\because R=1]$
$\Rightarrow V^{2} =16\, m / s ^{2}$
$\therefore$ Speed of the particle $v=4\, m / s$