First slide

Simple hormonic motion

Question

A small sphere is suspended by a string of length l. The sphere is making oscillatory motion between extreme positions A and B then

Moderate

A

Rate of work done by the gravitational force is zero at A, B and C.
B

work done by the tension in the string is always zero
C

both 1 and 2 are wrong
D

both 1 and 2 are right

Solution

At the extreme positions A and B, velocity is zero. Tension induced in the string is always perpendicular to the direction of motion. Since power delivered by tension is $\vec{T} . \vec{V}$ , it is always zero.
Power delivered by gravitational force is ${\vec{F}}_{g} . \vec{V}$ . At position C, $\vec{F_{g}}$ and $\vec{V}$ are mutually perpendicular and at the extreme positions $\vec{V}$ is zero. So option (1) is also right. Therefore, (4) is the correct option.

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