A rod $AB$ is shown in figure. End $A$ of the rod is fixed on the ground. Block is moving with velocity $\sqrt{3} \mathrm{m} {\mathrm{s}}^{-1}$ towards right. The velocity of end $B$ of rod when rod makes an angle of $60°$ with the ground is:

System is shown in figure and wedge is moving towards left with speed $2 \mathrm{m} {\mathrm{s}}^{-1}$. Then velocity of the block $B$ will be:

In the figure shown the velocity of lift is $2 \mathrm{m} {\mathrm{s}}^{-1}$ while string is winding on the motor shaft with velocity $2 \mathrm{m} {\mathrm{s}}^{-1}$ and block $A$ is moving downwards with a velocity of $2 \mathrm{m} {\mathrm{s}}^{-1}$, then find out the velocity of block $B$.

Two beads $A$ and $B$ move along a fixed semicircular wire frame as shown in figure. The beads are connected by an inelastic string which always remains tight. At an instant the speed of $A$ is $u$, $\angle BAC=45°$ and $\angle BOC=75°$, where $O$ is the centre of the semicircular arc. The speed of bead $B$ at that instant is:

Two masses $M_1$ and $M_2$ are attached to the ends of a light string which passes over a massless pulley attached to the top of a double inclined smooth plane of angles of inclination $\alpha$ and $\beta$. If $M_2>M_1$ and $\beta >\alpha$, then the acceleration of block $M_2$ down the inclined will be:

The pulley arrangements shown in figure are identical, the mass of the rope being negligible. In case I, the mass $m$ is lifted by attaching a mass $2m$ to the other end of the rope. In case II, the mass $m$ is lifted by pulling the other end of the rope with a constant downward force $F=2\mathrm{mg}$, where $g$ is acceleration due to gravity. The acceleration of mass in case I is: