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.

After the collision the fraction of energy lost by colliding body A is:

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: Collision between two billiard's ball are inelastic Reason: Momentum remains conserve during the collision

There is no loss in energy in elastic collision and Linear momentum is conserved in elastic collision.

The angular momentum must remain same in magnitude and direction when there is no torque acting on it. Thus, the plane of rotation must pass through the centre of earth.

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)

Consider the following figure, By angular momentum conservation, mV₀rₘₐₓ = mVrₘᵢₙ, V = V₀rₘₐₓ/rₘᵢₙ

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 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 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 block having mass m collides with an another stationary block having mass 2 m. The lighter block comes to rest after collision. If the velocity of first block is v, then the value of coefficient of restitution will must be

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) In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision. Reason (R) In elastic collision, the linear momentum of the system is conserved.

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.

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.

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

Assertion : For a system of particles under central force field, the total angular momentum is conserved. Reason : The torque acting on such a system is zero.

In an orbital motion, the angular momentum vector is

The direction of the angular velocity vector is along

Assertion : There are very small sporadic changes in the period of rotation of the earth. Reason : Shifting of large air masses in the earth's atmosphere produce a change in the moment of inertia of the earth causing its period of rotation to change.

Assertion : The earth is slowing down and as a result the moon is coming nearer to it. Reason : The angular momentum of the earth moon system is not conserved.

The angular momentum of a moving body remains constant if