Question

Figure. A.9 shows the direction of the total acceleration and velocity of a particle moving clockwise in a circle of radius $m$ at in instant of time. Tangential acceleration at this instant is $5m/s^2$. 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 $10m/s^2$.
• D. The particle is slowing down.

Answer 1

The correct option is D The particle is slowing down.

Since $a_1$ and $v$ are in the same direction, so the particle should be speeding up. So option(D) is wrong and option(B) is correct

$tan\left(30\right)=\frac{a_{tangential}}{a_{centripetal}}$

$\Rightarrow \frac{1}{\sqrt{3}}=\frac{5}{a_c}$

$\Rightarrow a_c=5\sqrt{3}m/s^2$ Option(A) is correct

Net acceleration is
$a=\sqrt{a_c^2+a_r^2}=\sqrt{(5\sqrt{3}{)}^2+5^2}=10m/s^2$ Option(C) is correct