Chapter Test: Rotational Motion - 2 JEE Physics Free MCQs

A section of fixed smooth circular track of radius R in vertical plane is shown in the figure. A block is released from position A and leaves the track at B. The radius of curvature of its trajectory when it just leaves the track at B is-

A particle is moving on a circular path with constant speed v. What is the change in its velocity after it has described an angle of 60º -

A cyclist starts from the centre O of a circular track of radius 1 km, reaches the edge A of the track and then cycles along the circumference and stops at point B as shown in the figure. If the total time taken is 10 min, what is the average velocity of the cyclist ?

A string of length L is fixed at one end and carries a mass M at the other end. The string makes 2/π revolutions per second around the vertical axis through the fixed end as shown in the figure, then tension in the string is -

When a ceiling fan is switched on, it makes 10 rotations in the first 3 second. How many rotations will it makes in the next 3 seconds? (Assume uniform angular acceleration)

A particle is given an initial speed u inside a smooth spherical shell of radius R =1 m that it is just able to complete the circle. Acceleration of the particle when its velocity is vertical is -

A non-uniform thin rod of length L is placed along x-axis as such its one of ends is at the origin. The linear mass density of rod is λ = λ₀x. The distance of centre of mass of rod from the origin is :

A body of mass 1 kg starts moving from rest at t = 0, in a circular path of radius 8 m. Its kinetic energy varies as a function of time as KE = 2t² J, where t is in seconds. Then -

Assertion : When a particle is moving in a circular path, both centripetal force and centrifugal force acts on the particle.

Reason : Centripetal force and centrifugal force depend on frame of reference.

The minimum velocity (in ms^–1) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction 0.6 to avoid skidding is-

A small block of mass m slides along a smooth frictional track as shown in the figure. (i) If it starts from rest at P, what is the resultant force  acting on it at Q? (ii) At what height above the bottom of the loop should the block be released so that the force it exerts against the track at the top of the loop equals its weight-

A simple pendulum consisting of a mass M attached in a string of length L is released from rest at an angle α. A pin is located at a distance l below the pivot point. When the pendulum swings down, the string hits the pin as shown in the figure. The maximum angle θ which string makes with the vertical after hitting the pin is –

A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position, and has a speed u. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is –

A wind farm generator uses a two-bladed propeller mounted on a pylon at a height of 20 m. The length of each propeller blade is 12 m. A tip of the propeller breaks off when the propeller is vertical. At that instant, the period of the motion of the propeller is 1.2 second. The fragment files off horizontally, falls and strikes the ground at point P.

In figure, the distance from the base of the pylon to the point where the fragment strikes the ground is closest to -

A small sphere is given vertical velocity of magnitude v₀ = 5m/s and it swings in vertical plane about end of massless string. If max.tension string can withstand is equal to twice of weight of sphere, then angle 'θ' with vertical at which string will break is -

The magnitude of displacement of a particle moving in a circle of radius a with constant angular speed ω varies with time t as –

The minimum velocity (in m/s) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction 0.6 to avoid skidding is-

A block of mass m is placed at the top of a smooth wedge ABC. The wedge is rotated about an axis passing through C as shown in the figure. The minimum value of angular speed ω such that the block does not slip on the wedge is-

A particle of mass m₁ is fastened to one end of a string and one of m₂ to the middle point, the other end of the string being fastened to a fixed point on a smooth horizontal table. The particle are then projected, so that the two portions of the string are always in the same straight line and describes horizontal circles. Find the ratio of tensions in the two parts of the string

A body of mass m slides down an incline and reaches the bottom with a velocity v. If the same mass were in the form of a ring which rolls down this incline, the velocity of the ring at the bottom would have been

The M.I. of a disc about its diameter is 2 units. Its M.I. about axis through a point on its rim and in the plane of the disc is

Three rings, each of mass P and radius Q are arranged as shown in the figure. The moment of inertia of the arrangement about YY' axis will be

Let I_A and I_B be moments of inertia of a body about two axes A and B respectively. The axis A passes through the centre of mass of the body but B does not.

Moment of inertia of a thin semicircular disc (mass = M & radius = R) about an axis through point O and perpendicular to plane of disc, is given by :

A rod of length 'L' is hinged from one end. It is brought to a horizontal position and released. The angular velocity of the rod when it is in vertical position is