Question

Diagram shows the direction of the total acceleration and velocity of a particle moving clockwise in a circle of radius 5/√3 m at an instant of time. Tangential acceleration at this instant is 5 m/s². Which of the following statements is not correct?

• A. The centripetal acceleration is $5\sqrt{3}$$m/s^2$
• B. Particle is speeding up
• C. The net acceleration is 10 $m/s^2$
• D. The particle is slowing down

Answer 1

Answer: (B), (D)

The particle is slowing down

since tangential acceleration and v are in same direction, so particle should be speeding up.

$tan{30}^{\circ }=\frac{a_t}{a_c}$
$\Rightarrow \frac{1}{\sqrt{3}}=\frac{5}{a_c}\Rightarrow$
$a_c=5\sqrt{3}m/s^2$
Net acceleration
$a=\sqrt{a_c^2+a_t^2}=\sqrt{(5\sqrt{3}{)}^2+5^2}=10m/s^2$