Q.389. Simple Pendulum.

Question 389.
The string of the pendulum of mass m and length can withstand a tension of 2mg at the maximum. How much angular displacement can be given to the pendulum?

Answer 389.
Tension will be maximum at the lowest point.
If T = maxm. tension
T - mg = mv^2/l
=> 2mg - mg = mv^2/l
=> mg = mv^2/l
=> KE = (1/2) mv^2 = (1/2) mgl

If θ = maximum angular displacement
rise of pendulum above its lowest point
= l(1 - cosθ)
PE at maximum angular displacement
= mgl(1 - cosθ)


KE converts to PE
=> (1/2) mgl = mgl(1 - cosθ)
=> 1 - cosθ = 1/2
=> cosθ = 1/2
=> θ = 60 degrees.

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