Two particles $A$ and $B$ initially at rest move towards each other under a mutual force of attraction. At the instant when speed of $A$ is $v$ and speed of $B$ is $2v$, speed of center of mass of the system is
Zero
$v$
$\frac{{3v}}{2}$
$3v$
A carpenter has constructed a toy as shown in the adjoining figure. If the density of the material of the sphere is $12$ $times$ that of the cone, the position of the centre of mass of the toy is given by
If the angular momentum of a body is increased by $200\,\%$ then increase in its rotational kinetic energy will be ....... $\%$.
Four particles of masses $1\,kg, 2 \,kg, 3 \,kg$ and $4\, kg$ are placed at the four vertices $A, B, C$ and $D$ of a square of side $1\, m$. The coordinates of centre of mass of the particles are
What is the moment of inhertia of a solid sphere of radius $R$ and density $\rho $ about its diameter ?
A thin circular ring of mass $M$ and radius $r$ is rotating about its axis with a constant angular velocity $\omega $ . Two objects each of mass $m$ are attached gently to the opposite ends of a diameter of the ring. The ring will now rotate with an angular velocity