Three identical rods of mass $M$ and length $L$ are placed on one another on the table so as to produce the maximum overhang as shown in figure. The maximum total overhang will be

Consider two skaters $A$ and $B$ initially at rest on ice (friction is negligible) with $A$ holding a ball. $A$ has greater mass than $B$ and the ball has some significant mass. $A$ throws the ball to $B.B$ catches it and throws it back to $A$ who catches it again. The magnitudes of the skater's (excluding ball) final velocities, momentum and kinetic energies (denoted below as $v, p$ and $K$ respectively) are related as

Two particles of equal mass $m$ are projected from the ground with speeds $v_1$ and $v_2$ at angles ${\theta }_1$ and ${\theta }_2$ as shown in the figure. Given ${\theta }_2>{\theta }_1$ and $v_1 \cos {\mathrm{\theta }}_1={\mathrm{v}}_2 \cos {\mathrm{\theta }}_2$. Which statement/s is/are correct?

A ball of mass $1 \mathrm{kg}$ is thrown up with an initial speed of $4 \mathrm{m}/\mathrm{s}.$ A second ball of mass $2 \mathrm{kg}$ is released from rest from some height as shown in figure. Choose the correct statement(s).

Two small rings, each of mass ' $\mathrm{m}$ ', are connected to the block of same mass ' $\mathrm{m}$ ' through an inextensible massless string of length ' $\mathrm{l}$ '. Rings are constrained to move over smooth rod $\mathrm{AB}.$ Initially, the system is held at rest as shown in figure. Let $\mathrm{u}$ and $\mathrm{v}$ be the velocities of ring and block, respectively when string makes an angle $60°$ with the vertical.

An ideal spring is permanently connected between two blocks of masses $\mathrm{M}$ and $\mathrm{m}.$ The blocks-spring system can move over a smooth horizontal table along a straight line along the length of the spring as shown in figure. The blocks are brought nearer to compress the spring and then released. In the subsequent motion,