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System of Particles and Rotational Motion

JEE Main 2024 (Online) 31st January Evening ShiftNumericalMedium📈 Topic in 19% papers+4
Ques. 1JEE Main 2024, 31 January (Evening Shift)

A body of mass 'm' is projected with a speed 'u' making an angle of 45 with the ground. The angular momentum of the body about the point of projection, at the highest point is expressed as 2mu3Xg. The value of 'X' is .

Answer

8

Solution

At the highest point velocity is horizontal, u 45 , at height H above O.

L=m(u 45 )H, where H= u2 2 45 2g= u24g

L=m u 2 u24g= mu34 2g= 2mu38g

X=8

Answer: 8

Keep practising — System of Particles and Rotational Motion

Ques. 2JEE Main 2024, 31 January (Evening Shift)

Two identical spheres each of mass 2 kg and radius 50 cm are fixed at the ends of a light rod so that the separation between the centers is 150 cm. Then, moment of inertia of the system about an axis perpendicular to the rod and passing through its middle point is x20 kgm2, where the value of x is .

Ques. 3JEE Main 2024, 30 January (Morning Shift)

A particle of mass m is projected with a velocity 'u' making an angle of 30 with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height h is :

  1. mu3 2 g
  2. zero
  3. 32 mu2g
  4. 316 mu3g
Ques. 4JEE Main 2024, 30 January (Morning Shift)

[figure] Consider a Disc of mass 5 kg, radius 2 m, rotating with angular velocity of 10 rad/s about an axis perpendicular to the plane of rotation. An identical disc is kept gently over the rotating disc along the same axis. The energy dissipated so that both the discs continue to rotate together without slipping is J.

Ques. 5JEE Main 2024, 30 January (Evening Shift)

Two discs of moment of inertia I1=4 kg m2 and I2=2 kg m2, about their central axes & normal to their planes, rotating with angular speeds 10 rad/s & 4 rad/s respectively are brought into contact face to face with their axes of rotation coincident. The loss in kinetic energy of the system in the process is J.

Ques. 6JEE Main 2024, 29 January (Morning Shift)

A cylinder is rolling down on an inclined plane of inclination 60 . Its acceleration during rolling down will be x 3 m/s2, where x= (use g=10 m/s2).

Ques. 7JEE Main 2024, 29 January (Evening Shift)

A body of mass 5 kg moving with a uniform speed 3 2 ms-1 in X-Y plane along the line y=x+4. The angular momentum of the particle about the origin will be kg m2 s-1.

Ques. 8JEE Main 2024, 27 January (Morning Shift)

Four particles each of mass 1 kg are placed at four corners of a square of side 2 m. Moment of inertia of system about an axis perpendicular to its plane and passing through one of its vertex is kg m2. [figure]

Ques. 9JEE Main 2024, 27 January (Evening Shift)

A heavy iron bar of weight 12 kg is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle 60 with the horizontal, the weight experienced by the man is :

  1. 3 kg
  2. 6 kg
  3. 6 3 kg
  4. 12 kg
Ques. 10JEE Main 2024, 27 January (Evening Shift)

A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of their kinetic energies is 7x, where x is .

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