Two rings of the same radius and mass are placed such that their centres are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to the plane of one of the rings is : (mass of the ring $= m,$ radius $= r$ )
$(1/2)\,\,mr^2$
$mr^2$
$(3/2)\,\,mr^2$
$2mr^2$
Two blocks which are connected to each other by means of a massless string are placed on two inclined planes as shown in fig. After releasing from rest, the magnitude of acceleration of the centre of mass of both the blocks is $(g = 10\, m/s^2)$
Two particles $A$ and $B$ initially at rest move towards each other under a mutual force of attraction. At the instant when velocity of $A$ is $v$ and that of $B$ is $2v$, the velocity of centre of mass of the system :
A $T$ shaped object with dimensions shown in the figure, is lying a smooth floor. A force $'\vec F'$ is applied at the point $P$ parallel to $AB,$ such that the object has only the translational motion without rotation. Find the location of $P$ with respect to $C$
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
The linear mass density of a rod of length $L$ varies as $\lambda = kx^2$, where $k$ is a constant and $x$ is the distance from one end. The position of centre of mass of the rod is