Answer:
Explanation:
For pendulum , time period is
T = 2π √ l / g
T² = 4π² l/ g
l = / g T² / 4π²
= 9.8 x 5² / 4π²
= 6.21 m
Angular impulse = Torque x time
= 30 x 6.21 x .3 = increase in angular momentum
30 x 6.21 x .3 = I ω ; I is moment of inertia and ω is angular velocity .
I ω = 55.89
I = 1/3 m l²
= 1/3 x 5 x 6.21²
= 64.27
Angular kinetic energy = 1/2 I ω²
= 1/2(I ω)²/ I
= .5x 55.89²/ 64.27
= 24.30 J
Due to it , the centre of mass of pendulum increases by height h so that
h = l/2 ( 1 - cos θ )
1/2 I ω² = mg l/2 ( 1 - cos θ)
24.3 = 5 x 9.8 x 3.1 ( 1 - cos θ)
( 1 - cos θ) = .16
cos θ = .84
θ = 33 degree.
