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|

Question

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 (A) 1, 2 and 3 are correct (B) 1 and 2 are correct (C) 2 and 4 are correct (D) 1 and 3 are correct

Tardigrade Admin · Accepted Answer

From die figure it is clear that T-M g cos θ= centripetal force T-M g cos θ=(M v2/L) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/fc59383d846d2fc1a683125dd3916b93-.png" /> Also, tangential acceleration |aT|=g sin θ.

1, 2 and 3 are correct

1 and 2 are correct

2 and 4 are correct

1 and 3 are correct

From die figure it is clear that T−Mgcosθ= centripetal force T−Mgcosθ=LMv2​ Also, tangential acceleration ∣aT​∣=gsinθ.

From die figure it is clear that
$T - M g cos θ =$ centripetal force
$T - M g cos θ = \frac{M v ^{2}}{L}$

Also, tangential acceleration $∣ a_{T} ∣ = g sin θ$ .