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13.Oscillations
hard
A simple pendulum of length $L$ and mass (bob) $M$ is oscillating in a plane about a vertical line between angular limits $ - \varphi $ and $ + \varphi $. For an angular displacement $\theta (|\theta | < \varphi )$, the tension in the string and the velocity of the bob are $T$ and $ v$ respectively. The following relations hold good under the above conditions
A
$T\cos \theta = Mg$
B
$T - Mg\cos \theta = \frac{{M{v^2}}}{L}$
C
The magnitude of the tangential acceleration of the bob $|{a_T}|\, = g\sin \theta $
D
Both (b) and (c)
(IIT-1986)
Solution
(d) From following figure it is clear that
$T – Mg\cos \theta = $Centripetal force
$ \Rightarrow T – Mg\cos \theta = \frac{{M{v^2}}}{L}$
Also tangential acceleration $|{a_r}| = g\sin \theta $.
Standard 11
Physics
