Assertion (A): A ball tied by thread is undergoing circular motion (of radius R) in a vertical plane.(Thread always remains in vertical plane). The difference of maximum and minimum tension in thread is independent of speed (u) of ball at the lowest position (u>5gR).Reason(R): For a ball of mass m tied by thread undergoing vertical circular motion (of radius R), difference in maximum and minimum magnitude of centripetal acceleration of the ball is independent of speed (u) of ball at the lowest position (u>5gR).

TA−TB=mg+mVA2l−(mVB2l−mg) =2mg+mvA2l−mVB2l =2mg+aCPB−aCPB=ml(vA2−VB2)=ml(4gl)=4 mg independent of speeds

Assertion (A): A ball tied by thread is undergoing circular motion (of radius R) in a vertical plane.(Thread always remains in vertical plane). The difference of maximum and minimum tension in thread is independent of speed (u) of ball at the lowest position (u>5gR).Reason(R): For a ball of mass m tied by thread undergoing vertical circular motion (of radius R), difference in maximum and minimum magnitude of centripetal acceleration of the ball is independent of speed (u) of ball at the lowest position (u>5gR).

TA−TB=mg+mVA2l−(mVB2l−mg) =2mg+mvA2l−mVB2l =2mg+aCPB−aCPB=ml(vA2−VB2)=ml(4gl)=4 mg independent of speeds

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Assertion (A): A ball tied by thread is undergoing circular motion (of radius R) in a vertical plane.(Thread always remains in vertical plane). The difference of maximum and minimum tension in thread is independent of speed $(u)$ of ball at the lowest position $(u > \sqrt{5 g R}) .$
Reason(R): For a ball of mass m tied by thread undergoing vertical circular motion (of radius R), difference in maximum and minimum magnitude of centripetal acceleration of the ball is independent of speed $(u)$ of ball at the lowest position $(u > \sqrt{5 g R}) .$

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If both Assertion and Reason are correct and Reason is the correct explanation of Assertion

If both Assertion and Reason are correct but reason is not the correct explanation of Assertion.

If Assertion is correct but Reason is incorrect.

If Assertion is incorrect but Reason is correct.

answer is A.

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Detailed Solution

$T_{A} - T_{B} = m g + \frac{m V_{A}^{2}}{l} - (\frac{m V_{B}^{2}}{l} - m g) = 2 m g + \frac{m v_{A}^{2}}{l} - \frac{m V_{B}^{2}}{l} = 2 m g + a_{C P B} - a_{C P B} = \frac{m}{l} (v_{A}^{2} - V_{B}^{2}) = \frac{m}{l} (4 g l)$

=4 mg independent of speeds

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