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Given below are two statements: one is labelled as Assertion (A) and other is labelled as Reason (R). Assertion (A): At highest position in a verti
Question

Given below are two statements: one is labelled as Assertion (A) and other is labelled as Reason (R).
Assertion (A): At highest position in a vertical circular motion, tension in the string is minimum.
Reason (R) : At the highest point, the tension = centrifugal force - weight of body. This is the minimum value for tension throughout the motion.

A.

Both (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

D.

None of the above is correct

Correct option is A

The correct answer is (a) Both (A) and (R) are correct and (R) is the correct explanation of (A)

Explanation:
• In vertical circular motion, at the highest point, both tension (T) and weight (mg) act downwards.
$T + mg = \frac{mv^2}{r}$ (centripetal force).
• Rearranging, $T = \frac{mv^2}{r} - mg$. Since weight opposes the centripetal requirement here, tension is at its minimum.
• At the lowest point, $T = \frac{mv^2}{r} + mg$, which is maximum.

Information Booster:
• For the body to complete the circle, the minimum velocity at the top must be $\sqrt{gr}$.
• At this critical velocity, tension at the top becomes zero.

Additional Knowledge:
(A) correct but (R) incorrect (Option b)
• Incorrect because the formula in (R) correctly explains the physics of (A).
(A) incorrect (Option c)
• Incorrect as tension is mathematically proven to be lowest at the top.
None (Option d)
• Incorrect as the physics is sound.

So the correct answer is (a)

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