We have two spheres one of which is hollow and the other solid. They have identical masses and moment of inertia about their respectively diameters. The ratio of their radius is given by
$5 : 7$
$3 : 5$
$\sqrt 3 :\sqrt 5 $
$\sqrt 3 :\sqrt 7 $
Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are $v$ and $2v$ at any instant, then the speed of centre of mass of the system will be
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.
In an experiment with a beam balance an unknown mass $m$ is balanced by two known masses of $16\,kg$ and $4\,kg$ as shown in figure. The value of the unknown mass $m$ is ....... $kg$
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
Two spheres are rolling with same velocity (for their $C. M.$) their ratio of kinetic energy is $2 : 1$ & radius ratio is $2 : 1$, their mass ratio will be :