AIIMS Physics System Of Particles And Rotational Motion Class 11 Questions

A disc of radius 5 m is rotating with angular frequency 10 rad/sec. A block of mass 2 kg to be put on the disc friction coefficient between disc and block is μₖ = 0.4, then find the maximum distance from axis where the block can be placed without sliding:

Given $V_{\text{CM}} = 2 \text{ m/s}$, $m = 2 \text{ kg}$, $R = 4 \text{ m}$. (A ring is shown in the x-y plane, rolling on the positive x-axis. Its center of mass is moving with velocity $v$ in the positive x-direction.) Find angular momentum of ring about origin if it is in pure rolling.

Given V_CM = 2 m/s, m = 2 kg, R = 4 m. Find angular momentum of ring about origin if it is in pure rolling.

A wheel having moment of inertia 2 kg-m² about its vertical axis, rotates at the rate of 60 rpm about this axis. The torque which can stop the wheel’s rotation in one minute would be

Ratio of total energy and rotational kinetic energy in the motion of a disc is

Assertion: The centre of mass of a proton and an electron, released from their respective positions remains at rest. Reason: The centre of mass remains at rest, if no external force is applied.

An elevator is going up with an acceleration 2 m/s². If radius of the wheel attached to the elevator is 0.1 m, then find out number of revolutions in t = 10 s.

What is the distance of centre of mass of a half ring from centre if the ring has radius = 0.5 m

A cart has mass 1 metric ton and sand of 1 metric ton is inside the cart. Now sand starts to leak at a rate of 0.5 kg/sec then, what will be velocity of cart so that total sand has come out from the cart.

A uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated uniformly to raise its temperature slightly, then

A uniform disc is acted by two equal forces of magnitude F. One of them, acts tangentially to the disc, while other one is acting at the central point of the disc. The friction between disc surface and ground surface is nF. If r be the radius of the disc, then the value of n would be (in N)

The minimum and maximum distance of a planet from the sun are $r_{\text{min}}$ and $r_{\text{max}}$. If the velocity at $r_{\text{max}}$ is $V_0$, then find the velocity at $r_{\text{min}}$.

A massless rod having length 2l has equal point masses attached to its two ends shown in figure. The rod is rotating about its axis passing through its centre and making angle θ with the axis. The magnitude change of momentum of rod i.e. dL/dt equals

A hemispherical bowl of radius r is set rotating about its axis of symmetry in vertical. A small block kept in the bowl rotates with the bowl without slipping on its surface. If the surface of the bowl is smooth and the angle made by the radius through the block with the vertical is θ, then find the angular speed at which the ball is rotating.

Two objects P and Q initially at rest move towards each other under mutual force of attraction. At the instant when the velocity of P is v and that of Q is 2v, the velocity of centre of mass of the system is

A uniform sphere of mass 500 g rolls without slipping on a plane surface so that its centre moves at a speed of 0.02 m/s. The total kinetic energy of rolling sphere would be (in J)

Assertion: An ice-skater stretches out arms-legs during performance. Reason: Stretching out arms-legs helps the performer to balance his or her body so that he or she does not fall.

Assertion: Torque on a body can be zero even if there is a net force on it. Reason: Torque and force on a body are always perpendicular.

Assertion: When a sphere is rolls on a horizontal table it slows down and eventually stops. Reason: When the sphere rolls on the table, both the sphere and the surface deform near the contact. As a result, the normal force does not pass through the centre and provide an angular declaration.

A liquid of mass M is filled in a container of length L and rotated with an angular velocity ω. The force exerted by the liquid at the other end

In the following questions, a statement of assertion is given followed by a corresponding statement of reason. Assertion: The total kinetic energy of a rolling solid sphere is the sum of rotational and translational kinetic energy. Reason: For all solid bodies, total kinetic energy is always twice of translational kinetic energy.

Assertion: The total kinetic energy of a rolling solid sphere is the sum of translational and rotational kinetic energies. Reason: For all solid bodies, total kinetic energy is always twice of translational kinetic energy.

A sphere of mass 10 kg and radius 0.5 m rotates about a tangent. The moment of inertia of the sphere is

Assertion : Value of radius of gyration of a body depends on axis of rotation.

A hemispherical bowl of radius r is set rotating about its axis of symmetry in vertical. A small block kept in the bowl rotates with bowl without slipping on its surface. If the surface of the bowl is smooth and the angle made by the radius through the block with the vertical is θ, then find the angular speed at which the ball is rotating.

A uniform sphere of mass 500 g rolls without slipping on a plane surface so that its centre moves at speed of 0.002 m/s. The total kinetic energy of rolling sphere would be (in J)

Assertion (A) If there is no external torque on a body about its centre of mass, then the velocity of the centre of mass remains constant. Reason (R) The linear momentum of an isolated system remains constant.

Assertion If the ice on the polar caps of the earth melts, then length of day will increase. Reason Moment of inertia of the earth increases, as ice on polar caps melts.

Dimensional formula of angular momentum is

Relation between magnetic moment and angular velocity is

Assertion: Moment of inertia is always constant. Reason: Angular moment is conserved that is why moment of inertia is constant.

Assertion: Centre of mass of a system does not move under the action of internal forces. Reason: Internal forces are non conservative forces.

If 2 kg mass is rotating on a circular path of radius 0.8 m with angular velocity of 44 rad/sec. If the radius of the path becomes 1 m, then what will be the value of angular velocity?

A solid cylinder, a circular disc, a solid sphere and a hollow cylinder of the same radius are placed on an inclined plane. Which of the following will have maximum acceleration at the bottom of the plane?

What is the moment of inertia for a solid sphere w.r.t. a tangent touching to its surface?

Given, ω̅ = 2k̂ and r̅ = 2î + 2ĵ. Find the linear velocity.

What is moment of inertia of a cylinder of radius r, along its height?

Four holes of radius R are cut from a thin square plate of side 4R and mass M. The moment of inertia of the remaining portion about z-axis is

Assertion: A wheel moving down a perfectly frictionless inclined plane will undergo slipping (not rolling motion). Reason: For perfect rolling motion, work done against friction is zero.

Assertion: A hollow shaft is found to be stronger than a solid shaft made of same material. Reason: The torque required to produce a given twist in hollow cylinder is greater than that required to twist a solid cylinder of same size and material.

A particle of mass m moves with constant speed along a circular path of radius r under the action of force F. Its speed is

Side of an equilateral triangle is l. Three point masses, each of magnitude m, are placed at the three vertices of the triangle. Moment of inertia of this system about one side of the triangle as axis is given by

If a solid sphere of mass 1 kg and radius 0.1 m rolls without slipping at a uniform velocity of 1 m/s along a straight line on a horizontal floor, the kinetic energy is

In the diagram shown below all three rods are of equal length L and equal mass M. The system is rotated such that rod B is the axis. What is the moment of inertia of the system?

The direction of the angular velocity vector is along

The moment of inertia of a rod about an axis through its centre and perpendicular to it is \( \frac{1}{12} ML^2 \) (where M is the mass and L, the length of the rod). The rod is bent in the middle so that the two halves make an angle of 60°. The moment of inertia of the bent rod about the same axis would be

Assertion : A judo fighter in order to throw his opponent on to the mat tries to initially bend his opponent and then rotate him around his hip. Reason : As the mass of the opponent is brought closer to the fighter’s hip, the force required to throw the opponent is reduced.

A given shaped glass tube having uniform cross section is filled with water and is mounted on a rotatable shaft as shown in figure. If the tube is rotated with a constant angular velocity ω when

A solid sphere is rolling on a frictionless surface, shown in figure with a translational velocity v m/s. If it is to climb the inclined surface then v should be

A horizontal platform is rotating with uniform angular velocity around the vertical axis passing through its centre. At some instant of time a viscous fluid of mass m is dropped at the centre and is allowed to spread out and finally fall. The angular velocity during this period