Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): At the highest position in a vertical circular motion, the tension in the string is minimum.
Reason (R): At the highest point, the tension = centrifugal force − weight of the body. This is the minimum value of the tension throughout the motion.
In the light of the above statements, choose the most appropriate answer from the options given below:
- ABoth (A) and (R) are correct and (R) is the correct explanation of (A)
- B(A) is correct but (R) is incorrect
- C(A) is incorrect but (R) is correct
- DNone of the above is correct
Show answer and explanation
Correct answers: (a) Both (A) and (R) are correct and (R) is the correct explanation of (A) or (b) (A) is correct but (R) is incorrect
Explanation
(A) is true. At the top of a vertical circle, the weight acts towards the centre along with the tension, so the string has to supply the least force there. The speed is also lowest at the top. So the tension is minimum at the highest point.
At the top, the forces towards the centre give the needed centripetal force: T + mg = mv²/r, so T = mv²/r − mg.
(R) writes this as "centrifugal force − weight". In an inertial frame there is no centrifugal force, so the book's key treats (R) as incorrect and gives (b). But in a frame moving with the body, mv²/r acts outwards as the centrifugal force, and (R)'s formula and its claim (minimum tension) are then right. So (a) can also be argued.
The book's key is (b), because (R) uses the centrifugal force, a pseudo-force. But in a frame moving with the body, (R)'s formula T = mv²/r − mg is correct, so (a) is also accepted.