HARD
JEE Main/Advance
IMPORTANT
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In the system as shown in figure, AB is a uniform rod of mass 10 kg and BC is a light string which is connected between wall and rod, in vertical plane. There is block of mass 15 kg connected at B with a light string. [Take g=10 m s-2] (BC and BD are two different strings)

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(i) Tension in the string BC

(ii) Hinge force exerted on beam at point A

Important Questions on Rotational Mechanics

MEDIUM
JEE Main/Advance
IMPORTANT

A rod of negligible mass having length l=2 m is pivoted at its centre and two masses of m1=6 kg and m2=3 kg are hung from the ends as shown in figure.

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(a) Find the initial angular acceleration of the rod if it is horizontal initially.

(b) If the rod is uniform and has a mass of m3=3 kg. 

(i) Find the initial angular acceleration of the rod.

(ii) Find the tension in the supports to the blocks of mass 3 kg and 6 kg  (g=10 ms-2).

HARD
JEE Main/Advance
IMPORTANT

The uniform rod AB of mass m is released from rest when β= 60º. Assuming that the friction force between end A and the surface is large enough to prevent sliding, determine (for the instant just after release)

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(a) The angular acceleration of the rod

(b) The normal reaction and the friction force at A.

HARD
JEE Main/Advance
IMPORTANT

A uniform thin rod of length L is hinged about one of its ends and is free to rotate about the hinge without friction. Neglect the effect of gravity.A force F is applied at a distance x from the hinge on the rod such that force is always perpendicular to the rod. Find the normal reaction at the hinge as function of x, at the initial instant when the angular velocity of rod is zero.

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HARD
JEE Main/Advance
IMPORTANT

A solid cylinder of mass M=1 kg & radius R=0.5 m is pivoted at its centre & has three particles of mass m=0.1kg mounted at its perimeter in the vertical plane as shown in the figure. The system is initially at rest. Find the angular speed of the cylinder, when it has swung through 900 in anticlockwise direction. [Take g=10 m s-2]

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HARD
JEE Main/Advance
IMPORTANT

A rigid body is made of three identical uniform thin rods each of length L fastened together in the form of letter H. The body is free to rotate about a fixed horizontal axis AB that passes through one of the legs of the H. The body is allowed to fall from rest from a position in which the plane of H is horizontal. What is the angular speed of the body, when the plane of H is vertical. 

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MEDIUM
JEE Main/Advance
IMPORTANT

A uniform rod of mass m and length L lies radially on a disc rotating with angular speed ω in a horizontal plane about its axis. The rod does not slip on the disc and the centre of the rod is at a distance R from the centre of the disc. Find out the kinetic energy of the rod.

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MEDIUM
JEE Main/Advance
IMPORTANT

The moment of inertia of the pulley system as shown in figure is 3 kgm2 . Its radius is 1m. The system is released from rest ,find the linear velocity of the block when it has descended through 40 cm. (Assume that there is no slipping between string & pulley and string is light) [Take g=10 m s-2 ]

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MEDIUM
JEE Main/Advance
IMPORTANT
A particle having mass 2 kg is moving with velocity (2i^+3j^) m s-1. Find angular momentum of the particle about origin when it is at (1, 1, 0).