Question

A ball tied to the end of the string swings in a vertical circle under the influence of gravity.

• A. When the string makes an angle ${90}^{\circ }$ with the vertical, the tangential acceleration is zero and radial acceleration is somewhere between minimum and maximum.
• B. When the string makes an angle ${90}^{\circ }$ with the vertical, the tangential acceleration is maximum and radial acceleration is somewhere between maximum and minimum.
• C. At no place in circular motion, tangential acceleration is equal to radial acceleration.
• D. When radial acceleration has its maximum value, the tangential acceleration is zero.

Answer 1

Answer: (B), (D)

When the string makes an angle ${90}^{\circ }$ with the vertical, the tangential acceleration is maximum and radial acceleration is somewhere between maximum and minimum.
When radial acceleration has its maximum value, the tangential acceleration is zero.

$AandB:\left|a_{tangential}\right|=g$ which is maximum and radial acceleration is between\ maximum and minimum when string makes ${90}^0$.

$\Rightarrow$ A is not correct, B is correct. C is not correct as tangential acceleration and radial acceleration can become equal multiple times in a circular motion.D is correct because radial acceleration becomes maximum at the bottom most point where tangential acceleration is zero.