An massless equilateral triangle EFG of side ‘a’ (As shown in figure) has three particles of mass m situated at its vertices. The moment of inertia of the system about the line EX perpendicular to EG in the plane of EFG is $${N \over {20}}$$ ma² where N is an integer. The value of N is _____.

A person of 80 kg mass is standing on the rim of a circular platform of mass 200 kg rotating about its axis at 5 revolutions per minute (rpm). The person now starts moving towards the centre of the platform. What will be the rotational speed (in rpm) of the platform when the person reaches its centre _________.

One end of a straight uniform 1m long bar is pivoted on horizontal table. It is released from rest when it makes an angle 30º from the horizontal (see figure). Its angular speed when it hits the table is given as $$\sqrt n $$ s^-1, where n is an integer. The value of n is _________.

A body of mass m = 10 kg is attached to one end of a wire of length 0.3 m. The maximum angular speed (in rad s^–1) with which it can be rotated about its other end in space station is :
(Breaking stress of wire = 4.8 × 10⁷ Nm^–2 and
area of cross-section of the wire = 10^–2 cm²) is: