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
$L_A < L_B$
$L_A = L_B$
$L_A \ne L_B$
the relationship between $L_A$ and $L_B$ depends upon the slope of the line $AB$
$A$ non uniform rod $OA$ of linear mass density $\lambda = \lambda_0x$ $(\lambda_0 =$ const.) is suspended from ceiling with hinge joint $O$ & light string as shown in figure. Find the angular acceleration of rod just after the string is cut.
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
A rigid body is rotating with variable angular velocity $(a -bt)$ at any instant of time $t.$ The total angle subtended by it before coming to rest will be ( $a$ and $b$ are constants)
A circular disc of radius $R$ has a uniform thickness. A circular hole of diameter equal to the radius of disc has been cut out as shown. Distance of centre of mass of the remaining disc from point $O$ is
A child is standing at one end of a long trolley moving with a speed $v$ on a smooth horizontal floor. If the child starts running towards the other end of the trolley with a speed $u$, the centre of mass of the system (trolley + child) will move with a speed.