NEET Physics Systems Of Particles And Rotational Motion MCQs

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:

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 rod of length $L$ and mass $M$ is rotating freely with an angular velocity $\omega$ about an axis perpendicular to the rod and passing through one end. A particle of mass $m$ moving with velocity $v$ perpendicular to the rod strikes the other end and sticks to it. The new angular velocity of the system is:

Two discs of same thickness but different radii are rotating about their respective axes perpendicular to the plane and passing through the centre. The ratio of their radii is 2:1. If their kinetic energies of rotation are same, the ratio of their angular momenta is:

A thin uniform rod of mass M and length L is rotating with angular velocity $\omega$ about an axis perpendicular to the rod and passing through one of its ends. A small particle of mass m moving with velocity v perpendicular to the rod collides with the rod at a distance x from the axis of rotation and sticks to it. The new angular velocity of the system is:

A disc of mass M and radius R is rotating about its axis with angular velocity $\omega$. If a small portion of mass m is detached from the rim of the disc, the new angular velocity of the remaining disc will be:

Two identical discs are rotating about their axes with angular speeds $\omega_1$ and $\omega_2$. They are brought into contact face to face with their axes of rotation coincident. The final angular speed of the system is:

A thin uniform rod of mass $M$ and length $L$ is rotating freely with angular speed $\omega_0$ about an axis perpendicular to the rod and passing through one end. A particle of mass $m$ traveling with velocity $v_0$ hits the rod at a distance $L/2$ from the axis and sticks to it. The new angular speed of the system is:

A solid sphere is rotating freely about an axis through its center. If its radius is doubled while keeping its mass constant, its angular momentum will:

A particle of mass $m$ moves in a circular orbit of radius $r$ under the influence of a central force whose potential energy is given by $U(r) = kr^3$, where $k$ is a constant. The angular momentum of the particle is: