Chapter Test: Rotational Motion - 1 JEE Physics Free MCQs

A string of length 1m is fixed at one end with a bob of mass 100 g and the string makes 2/π rev/s around a vertical axis through a fixed point. The angle of inclination of the string with vertical is-

A particle of mass m revolves in a circle of radius r with a uniform speed ν, then its velocity vector -

A pendulum consisting of a small sphere of mass M suspended by an inextensible and massless string of length l is made to swing in a vertical plane. If the breaking strength of the string is 2Mg, then the maximum angular amplitude of the displacement form the vertical can be -

In Q. no. 53, the angular velocity and angular acceleration of the particle are -

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 particle crosses the topmost point C of a vertical circle with critical speed; then the ratio of velocities at points A, B and C is -

A block is rotating in a circular track and angular speed of the block is given by ω = at². Where ω is in rad/s and t is in seconds, a is a constant and equal to 2 rad/s³. Mass of the block is 1 kg and radius of circular track is 1m. Net force acting on the block at t = 2s is -

A particle describes a horizontal circle in a conical funnel whose inner surface is smooth with speed of 0.5 m/s. What is the height of the plane of circle from vertex of the funnel ?

A heavy particle of mass m, oscillates through 180º inside of a smooth hemisphere of radius R as shown. If V is speed of particle at any instant, the normal reaction on it at that instant will be –

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

A stone hanging from a massless string of length 15 m is projected horizontally with speed 147 m/s. Then the speed of the particle at the point where tension in string equals the weight of particle is –

A ball is held at rest at position A by two light strings. The horizontal string is cut and the ball starts swinging as a pendulum point B is the farthest to the right the ball goes as it swings back and forth. What is the ratio of the tension in the supporting string in position B to its value at A before the horizontal string was cut.

A stone of mass 0.5 kg tied with a string of length 1 metre is moving in a circular path with a speed of 4 m s^–1.The tension acting on the string in newton is -

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. cceleration of the particle when its velocity is vertical is -

A particle moves in a circle of radius 0.25 m at two revolutions per second. The acceleration of the particle in metre second² is -

Four masses are fixed on a massless rod as shown fig. The moment of inertia about the axis P is about :  

A disc of radius b and mass m rolls down an inclined plane of vertical height h. the translational speed when it reaches the bottom of the plane will be 

Two rings of radius R and nR made up of same material have the ratio of moment of inertia about an axis passing through centre is 1 : 8. The value of n is

A solid sphere of radius R has moment of inertia I about its diameter. It is melted into a disc of radius r and thickness t. If its moment of inertia about the tangential axis (which is perpendicular to plane of the disc), is also equal to I, then the value of r and t are (respectively)

Point C is the centre of the rigid body shown in fig. Find the total torque acting on the body

about point C.(CW - clockwise ACW - anticlockwise)