System of Particles and Rotational MotionNEET Physics · Class 11 · NCERT Chapter 6

Two particles of masses $1\text{kg}$ and $3\text{kg}$ are at $x=0$ and $x=4\text{m}$ respectively. Their centre of mass is at:

Three particles of masses $1\text{kg}$, $2\text{kg}$ and $3\text{kg}$ are placed at the corners of an equilateral triangle of side $1\text{m}$. The centre of mass lies:

A bomb at rest explodes into two fragments of masses $1\text{kg}$ and $2\text{kg}$. The lighter fragment moves with velocity $6\text{m/s}$. The velocity of the heavier fragment is:

The moment of inertia of a thin uniform rod of mass $M$ and length $L$ about an axis through its centre and perpendicular to its length is:

The moment of inertia of a solid sphere of mass $M$ and radius $R$ about a diameter is:

The moment of inertia of a ring of mass $M$ and radius $R$ about a diameter is:

A thin rod of mass $M$ and length $L$ has moment of inertia $\frac{M{L}^2}{12}$ about its centre. Its moment of inertia about an axis through one end (perpendicular to the rod) is:

A circular disc of mass $M$ and radius $R$ has moment of inertia $\frac{M{R}^2}{2}$ about its central axis. Its moment of inertia about a tangent line in the plane of the disc is:

A figure skater rotates about a vertical axis with ${\omega }_1=6\text{rad/s}$. With arms outstretched, her moment of inertia is $I_1$. When she pulls her arms in, $I_2=I_1/3$. Her new angular velocity is:

A planet revolves around the Sun in an elliptical orbit. The physical quantity that remains constant is:

A particle of mass $m$ moves in a straight line with constant velocity $v$ at a perpendicular distance $d$ from a fixed point $O$. Its angular momentum about $O$ is:

A wheel of moment of inertia $2\text{kg}{\text{m}}^2$ has a torque of $4\text{N}\cdot \text{m}$ applied to it. The angular acceleration is:

A flywheel of moment of inertia $0.4\text{kg}{\text{m}}^2$ rotates at $10\text{rad/s}$. The kinetic energy of rotation is:

A solid sphere rolls down a smooth inclined plane of height $h$. Its speed at the bottom is:

A solid sphere, a hollow sphere, a disc and a ring (all of same mass and radius) roll down identical inclines from the same height. Which reaches the bottom first?

For a body rolling without slipping, the ratio of translational to rotational kinetic energy is largest for which of the following?

A force of $10\text{N}$ is applied at a perpendicular distance of $0.3\text{m}$ from the axis. The torque is:

A force $\vec{F}=3\hat{i}+4\hat{j}\text{N}$ acts at a position $\vec{r}=2\hat{i}\text{m}$. The torque is:

A wheel starts from rest and reaches angular velocity $20\text{rad/s}$ in $5\text{s}$ under a constant torque. Its angular acceleration is:

Three thin rods, each of mass $M$ and length $L$, form an equilateral triangle. The moment of inertia about an axis through the centroid perpendicular to the plane is:

A solid sphere of mass $m$ and radius $R$ rolls without slipping with speed $v$. Its total kinetic energy is:

A wheel of radius $R$ rolls without slipping with angular velocity $\omega$. The velocity of the topmost point of the wheel is:

From a uniform disc of radius $R$, a smaller disc of radius $R/2$ is cut out. Its centre is at $R/2$ from the centre of the original disc. The CoM of the remaining part is at:

A disc of moment of inertia $I_1$ rotating at $\omega$ is suddenly placed in contact with a stationary disc of moment of inertia $I_2$ on the same axis. They eventually rotate together. Their common angular velocity is:

A disc of mass $M$ and radius $R$ rotates about its centre with angular velocity $\omega$. The kinetic energy is:

If the line of action of a force passes through the axis of rotation, the torque about that axis is:

Angular momentum and Planck's constant share which dimensional formula?

Two spheres, both of mass $M$ and radius $R$, are connected by a thin rigid rod of negligible mass and length $2R$ (so the spheres touch each other). The moment of inertia about an axis perpendicular to the rod through its centre is:

A disc and a ring (same mass, same radius) roll down identical inclines from the same height. The ratio of their speeds at the bottom (disc : ring) is:

A man of mass $50\text{kg}$ stands on one end of a $10\text{m}$ long boat of mass $200\text{kg}$ in still water. He walks to the other end. Ignoring water resistance, the boat moves through (in opposite direction):

The moment of inertia of a uniform circular disc of mass $M$ and radius $R$ about a tangent perpendicular to the plane is: