A simple pendulum is oscillating between extreme position P and Q about the mean position O. Wchi of the following statements are true about the motion of pendulum?

Options

A. At point O, the acceleration of the bob is different from zero.
B. The acceleration of the bob is constant throughout the oscillation.
C. The tension in the string is contant throughout the oscillation.
D. The tension is maximum at O and minimum at P or Q.

Answer

A, D

Explanation

Statement (a) is correct. At any position O and P or between O and Q, there are two acceleration a tan gential acceleration `gsinalphs` and a centripetal acceleration `(v^2)/(l)` (because the pendulum moves along the arc of a circle or radiusl), where l is the length of the pendulum and v its speed at that position. When the bob is at the mean position O, the angle `alpha=0`, therefore `sinalpha=0`, hence the tengential acceleration is zero But at O, speed v is maximum and the centripetal acceleration `(v^2)/(l)` is directed radially towards the point of support. When the bob is at the end point P and Q, the speed v is zero, hence the centripetal acceleration is zero at the end point, but the tangential acceleration is maximum and is directed along the tangent to the curve at P and Q. The tension in the string is not contant throughout the oscillation. At any position between O and end point P or Q. The tension in the string is given by `T=mgcosalpha`.
At the end point P and Q, the value of `alpha` is the gretest, hence the tension is the least. At the mean position O, `alpha=0` and `alpha=1` which is the greatest, hence tension is greatest at the mean position.