Four masses each 2 kg are placed at the corners A, B, C, D of a mass less square frame. 40 kg mass is at the centre O of a square frame of side 0.2m. It is to be rotated about an axis passing through the centre O and perpendicular to the plane of the frame. Calculate the torque in N-m required to produce an angular acceleration of 2 rads⁻² .

Step-by-step solution

The distance of each corner from the centre of the square frame is: r = a 2 = 0.2 2 m The moment of inertia of the four masses (each of mass m = 2 kg ) at the corners about the axis passing through the centre and perpendicular to the plane is: I_ corners = 4 m r^2 = 4 2 ( 0.2 2 )^2 I_ corners = 8 0.04 2 = 0.16 kg m ^2 The 40 kg mass is placed exactly at the centre O (on the axis of rotation), so its distance from the axis is zero. Its moment of inertia is: I_ centre = 40 0^2 = 0 The total moment of inertia of the s