mω²sin²θ
2mω²sinθcosθ
mv²sin²θ
m(l/2)ωsinθcosθ
Correct option is B. mω²sin²θ
We know that the rate of change of angular momentum is equal to the torque acting on the system
⇒|dL/dt| = τ
From the figure, the force on the mass m is given as:
F = mrω² (Due to the centripetal force)
r = lsinα
⇒F = m * lsinα * ω²
⇒τ = r⊥ * F
r⊥ = lcosα
⇒τ = lcosα * m * lsinαω²
⇒τ = ml²ω²sinαcosα
Total torque due to both masses is given by
τnet = τ₁ + τ₂ = ml²ω²sinαcosα + ml²ω²sinαcosα
⇒τnet = 2ml²ω²sinαcosα = ml²ω²sin2α
∴|dL/dt| = τnet = ml²ω²sin2α