A particle of mass 100 g is projected at time t = 0 with a speed 20 m s⁻¹ at an angle 45° to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time t = 2 s is found to be √K kg m² s⁻¹. The value of K is ________. [Take g = 10 m s⁻²] Image
Physics · Circular Motion
JEE Mains 29 January 2023 Shift 2 Evening Shift

Question

A particle of mass 100 g is projected at time t = 0 with a speed 20 m s⁻¹ at an angle 45° to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time t = 2 s is found to be √K kg m² s⁻¹. The value of K is ________. [Take g = 10 m s⁻²] Image

Physics · Circular Motion

JEE Mains 29 January 2023 Shift 2 Evening Shift

G1 Physics · Accepted Answer

Torque about the origin is τ = mgx, where x = vₓt and vₓ = 20cos45° = 10√2 m s⁻¹. Angular momentum change L = ∫₀² τ dt = ∫₀² mgvₓt dt = mgvₓ(t²/2)|₀² = (0.1)(10)(10√2)(4/2) = 20√2 kg m² s⁻¹ = √800 kg m² s⁻¹. Hence K = 800.