Question

A simple pendulum is hanging from the roof. It is performing non-uniform circular motion, as it oscillates. Which of the options is incorrect regarding its motion?

• A. It comes to rest twice in one complete oscillation.
• B. When bob is at rest, its acceleration is non zero.
• C. When bob is in lowest position, speed is maximum.
• D. When bob is in lowest position, its acceleration is zero.

Answer 1

The correct option is D When bob is in lowest position, its acceleration is zero.

$1)$ At each extreme position, the velocity of bob is zero and in one oscillation, it comes twice at extreme points.

$2)$ At extreme position, the free body diagram is as follows.

The resultant of $T$ and $mg$ can not be zero
$\Rightarrow$ Acceleration is non-zero

$3)$ Since gravitational potential energy is minimum at lowest position.
$\Rightarrow$ Kinetic energy will be maximum.
$\Rightarrow$ Speed will be maximum.

$4)$ At the lowest position, acceleration is directed vertically downwards and its magnitude is, $a_c=\frac{v^2}{l}$ where, $v$ is the velocity of bob and $l$ is the length of pendulum. So, the acceleration is not zero at the lowest position.

Hence, $\left(D\right)$ is the correct answer.