A pendulum of length m having a bob of mass kg is hanging from a rigid support. If the bob is projected horizontally with a velocity m/s. The tension in the string is 6k Newton when angle made by the string is from vertical as shown. Find the value of

Question

A pendulum of length $ℓ = 1$ m having a bob of mass $m = 1$ kg is hanging from a rigid support. If the bob is projected horizontally with a velocity $v_{0} = \sqrt{35}$ m/s. The tension in the string is 6k Newton when angle made by the string is $60 °$ from vertical as shown. Find the value of $k$ .

Smart Achievers · Accepted Answer

(5)

$\frac{1}{2} m v_{0}^{2} = \frac{1}{2} m v^{2} + m g l (1 - \cos θ), T - m g \cos θ = \frac{m v^{2}}{R}$

Solution

Ans.
(5)

$\frac{1}{2} m v_{0}^{2} = \frac{1}{2} m v^{2} + m g l (1 - \cos θ), T - m g \cos θ = \frac{m v^{2}}{R}$

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Solution

Q. A pendulum of length ℓ=1 m having a bob of mass m=1 kg is hanging from a rigid support. If the bob is projected horizontally with a velocity v0=35 m/s. The tension in the string is 6k Newton when angle made by the string is 60° from vertical as shown. Find the value of k.

Ans. (5) 12mv02=12mv2+mgl(1-cosθ), T-mgcosθ=mv2R

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Ans.
(5)

$\frac{1}{2} m v_{0}^{2} = \frac{1}{2} m v^{2} + m g l (1 - \cos θ), T - m g \cos θ = \frac{m v^{2}}{R}$