A uniform rod AB of mass 2 kg and length 30 cm is at rest on a smooth horizontal surface. An impulse of force 0.2 N s is applied to end B. The time taken by the rod to turn through a right angle will be π/x s, where x = ____. Image
Physics · Rotational Motion · combined translatory and rotatory motion ,Pure rolling motion
JEE Mains 2024 01 Feb Evening Shift

Question

A uniform rod AB of mass 2 kg and length 30 cm is at rest on a smooth horizontal surface. An impulse of force 0.2 N s is applied to end B. The time taken by the rod to turn through a right angle will be π/x s, where x = ____. Image

Physics · Rotational Motion · combined translatory and rotatory motion ,Pure rolling motion

JEE Mains 2024 01 Feb Evening Shift

G1 Physics · Accepted Answer

Image Impulse: J = 0.2 N s Angular impulse about the centre: ΔL = (L/2)J = (0.3/2)(0.2) = 0.03 kg m² s⁻¹ Moment of inertia of rod about its centre: I = ML²/12 = 2(0.3)²/12 = 0.09/6 kg m² Using: ΔL = Iω 0.03 = (0.09/6)ω ω = 2 rad/s For rotation through a right angle: θ = π/2 t = θ/ω = (π/2)/2 = π/4 s Hence: x = 4