NEET Questions

Two bodies of masses $m_1$ and $m_2$ moving with velocities $u_1$ and $u_2$ respectively collide head-on elastically. After the collision, they move with velocities $v_1$ and $v_2$. Which of the following expressions is correct for the velocity of the center of mass?

In an elastic oblique collision between two identical particles, with one particle initially at rest, the angle between the velocities of the particles after the collision is $heta$. Which of the following is true about $heta$?

Two particles of masses $m_1$ and $m_2$ are connected by a light inextensible string passing over a smooth pulley. If the acceleration of the center of mass of the system is $g/4$, what is the ratio of the masses $m_1/m_2$?

A system consists of three particles of masses 1 kg, 2 kg, and 3 kg located at the vertices of an equilateral triangle of side $L$. If the 1 kg mass is removed, by what distance does the center of mass of the system shift?

A uniform rod of mass $M$ and length $L$ is bent into a semicircular ring. The coordinates of the center of mass of the semicircular ring are:

A dog of mass $m$ stands at one end of a flat boat of mass $M$ and length $L$ at rest on a frictionless surface of a lake. The dog walks to the other end of the boat and stops. The displacement of the center of mass of the boat-dog system is:

A particle of mass $m$ moves along a trajectory given by $\vec{r}(t) = (t - \sin(t))\hat{i} + (1 - \cos(t))\hat{j}$, where $t$ is time. The net force acting on the particle is:

Two blocks of masses $m$ and $2m$ are placed on a smooth horizontal surface and connected by a spring. If an impulse $J$ is applied to the lighter block, the velocity of the center of mass immediately after the impulse is:

A thin uniform rod of mass $M$ and length $L$ is bent into a semicircle. A particle of mass $m$ is placed at the center of the semicircle. The gravitational force exerted by the rod on the particle is:

Two particles of masses $m_1$ and $m_2$ are connected by a massless rigid rod of length $L$. The system rotates with a constant angular velocity $\omega$ about an axis perpendicular to the rod and passing through its center of mass. The kinetic energy of the system is: