1. Tardigrade
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  3. Physics
  4. A simple pendulum of length L and mass (bob) M is oscillating in a plane about a vertical line between angular limits -φ and +φ For an angular displacement θ(|θ|<φ) the tension in the string and the velocity of the bob ar T and v respectively. The following relations hold good (1) T=M g cos θ=(M v2) / L (2) T cos θ=M g (3) The magnitude of the tengential acceleration of the bob |aT|=g sin θ (4) T=M g cos θ

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Q. A simple pendulum of length $L$ and mass (bob) $M$ is oscillating in a plane about a vertical line between angular limits $-\phi$ and $+\phi$ For an angular displacement $\theta(|\theta|<\phi)$ the tension in the string and the velocity of the bob ar $T$ and $v$ respectively. The following relations hold good
(1) $T=M g \cos \theta=\left(M v^{2}\right) / L$
(2) $T \cos \theta=M g$
(3) The magnitude of the tengential acceleration of the bob $\left|a_{T}\right|=g \sin \theta$
(4) $T=M g \cos \theta$

BHUBHU 2009

Solution:

From die figure it is clear that
$T-M g \cos \theta=$ centripetal force
$T-M g \cos \theta=\frac{M v^{2}}{L}$
image
Also, tangential acceleration $\left|a_{T}\right|=g \sin \theta$.