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Q.

The bob of a simple pendulum is displaced from its equilibrium position O to a position Q which is at height h above O and the bob is then released. Assuming the mass of the bob to be m and time period of oscillations to be 2.0 sec, the tension in the string when the bob passes through O is

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a

m(g+π2gh)

b

m(g+π2gh)

c

m(g+π22gh)

d

m(g+π23gh)

answer is A.

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Detailed Solution

Tension in the string when bob passes through lowest point T = mg+mv2r = mg + mvω (∴ v = rω)putting v = 2gh and ω = 2πT = 2π2 = πwe get T = m(g+π2gh)
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The bob of a simple pendulum is displaced from its equilibrium position O to a position Q which is at height h above O and the bob is then released. Assuming the mass of the bob to be m and time period of oscillations to be 2.0 sec, the tension in the string when the bob passes through O is