Question

two particles of masses m and 2m are connected by a massless string of length 3 metre and whole system is rotating about their centre of mass with angular speed [omega] the kinetic energy of the system is​

Answer 1

Answer:

The kinetic energy of the system is 3mω²

Explanation:

Kinetic energy of the system = 1/2 (Iω²)

Where I is the moment of inertia of the system

To find the moment of inertia of the system we need to locate its centre of mass

Let centre of mass be located at distance x from the particle of mass m

then

(m+2m)x = m×0 + 2m × 3

or x = 6/3 = 2m (from the mass m)

The moment of inertia will be calculated around the axis passing through the centre of mass

Moment of Inertia I = m × 2² + 2m × 1² = 4m + 2m = 6m

Kinetic Energy = (1/2)Iω² = 1/2 × 6m × ω² = 3mω²

Answer 2

Answer:

correct ANSWER is 3mw^2