A constant torque acting on a uniform circular wheel changes its angular momentum from $L_0$ to $4L_0$ in $4\,s$ . The magnitude of this torque is

A string is wrapped around a disc of mass $M$ and radius $R$ and the free end is fixed to ceiling. Centre of mass falls down as the disc unwinds the string. The tension in the string is

Four particles of masses $m_1 = 2m, m_2 = 4m, m_3 = m$ and $m_4$ are placed at four corners of a square. What should be the value of $m_4$ so that the centres of mass of all the four particles are exactly at the centre of the square ?

In a gravity free space, a man of mass $M$ standing at a height $h$ above the floor, throws a ball of mass $m$ straight down with a speed $u$ . When the ball reaches the floor, the distance of the man above the floor will be

A particle of mass $m$ moves in the $XY$ plane with a velocity $V$ along the straight line $AB$ . If the angular momentum of the particle with respect to origin $O$ is $L_A$ when it is at $A$ and $L_B$ when it is at $B$ , then

Particles of masses $m, 2m, 3m, ...... nm$ $grams$ are placed on the same line at distances $l, 2l, 3l,...., nl\, cm$ from a fixed point. The distance of the centre of mass of the particles from the fixed point (in centimetres) is