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:

Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force F at a point b above its centre of mass (see figure). If the coefficient of friction is $$\mu $$ = 0.4, the maximum possible value of 100 × $${b \over a}$$ for box not to topple before moving is .......