First slide

Vertical circular motion

Question

The length of a simple pendulum is 50 cm and mass of its bob is 0.1 kg. The bob is given a velocity 5 m/s along horizontal direction when the bob is at lowest position and the bob describes vertical circle of radius equal to length of pendulum. The position in the vertical circle, where the tension in the string is 4.5 N is
(g = 10ms^–2)

Moderate

A

highest point
B

lowest point
C

at an angle 60⁰ from lowest point of vertical circle
D

at an angle of 60⁰ from highest point of vertical circle

Solution

$Tension at any point T = \frac{{mv}^{2}}{l} - 2 mg + 3 mgcosθ where v is the velocity at the lowest point 4.5 = 0.1 (\frac{5^{2}}{0.5} - 2 \times 10 + 3 \times 10 cosθ) 45 = 50 - 20 + 30 cosθ 15 = 30 cosθ cosθ = 1 / 2 θ = 60^{0} form the lowest point from the top point it is 180^{0} - 60^{0} = 120^{0}$

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