Three guns are aimed at the centre of a circle. They are mounted on the circle, $120°$ apart. They fire in a timed sequence, such that the three bullets collide at the centre and mash into a stationary lump. Two of the bullets have identical masses of $4.5 \mathrm{g}$ each and speed $v_1$ and $v_2$. The third bullet has a mass of $2.50 \mathrm{g}$ and a speed of $575{ \mathrm{ms}}^{-1}$. Find the unknown speeds.

A force-time graph for a linear motion of a body is shown in figure. The change in linear momentum between $0$ and $7\mathrm{s}$ is

Consider the following two statements :

I. Linear momentum of a system of particles is zero

II. Kinetic energy of a system of particles is zero.

Two blocks of mass $m$ and $2m$ are connected by a light string passing over a frictionless pulley. As shown in the Fig. $7.67$, the mass $m$ is placed on a smooth inclined plane of inclination $30°$ and $2m$ hangs vertically. If the system is released, the block moves with an acceleration equal to: