Hello,

Mass of solid cylinder , m = 2kg

Radius of cylinder , r = 4cm = 0.04m

A solid cylinder is rotating about its axis,

So, moment of inertia , I = 1/2 mr²

So, I = 1/2 × 2 × (0.04)² = 16 × 10^-4 Kgm²

= 1.6 × 10^-3 kgm²

Angular frequency,  = 3rpm = 3 × 2π/60 rad/s = π/10 rad/s

Angular displacement = 2π revolution

= 2π × 2π = 4π² [ as 1 revolution = 2π ]

From conservation of energy theorem,

Change in rotational kinetic energy = torque × angular displacement

So, 1/2 I = torque × 4π²

So, 1/2 × 1.6 × 10^-3 × 1/100 = torque × 4

Hence, Torque = 2 × 10^-6 Nm

Best Wishes.