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System of Particles and Rotational Motion

JEE Main 2025 (Online) 2nd April Evening ShiftMCQEasy📈 Topic in 19% papers+4−1
Ques. 1JEE Main 2025, 2 April (Evening Shift)

The moment of inertia of a circular ring of mass M and diameter r about a tangential axis lying in the plane of the ring is :

  1. 38Mr2
  2. 2Mr2
  3. 12Mr2
  4. 32Mr2

Answer

(1) 38Mr2

Solution

Radius of the ring R = r2

About a diameter (perpendicular axis theorem): Id = 12MR2

Tangent in the plane is parallel to a diameter at distance R (parallel axis theorem):

I = 12MR2 + MR2 = 32MR2

= 32M ( r2 )2 = 38Mr2

Answer: (1)

Keep practising — System of Particles and Rotational Motion

Ques. 2JEE Main 2025, 2 April (Evening Shift)

[figure] A wheel of radius 0.2 m rotates freely about its center when a string that is wrapped over its rim is pulled by a force of 10 N as shown in figure. The established torque produces an angular acceleration of 2 rad/s2. Moment of inertia of the wheel is kg m2. (Acceleration due to gravity = 10 m/s2)

Ques. 3JEE Main 2025, 29 January (Morning Shift)

The coordinates of a particle with respect to origin in a given reference frame is (1, 1, 1) meters. If a force of F = i - j + k acts on the particle, then the magnitude of torque (with respect to origin) in z-direction is .

Ques. 4JEE Main 2025, 29 January (Evening Shift)

[figure] Three equal masses m are kept at vertices (A, B, C) of an equilateral triangle of side a in free space. At t=0, they are given an initial velocity VA=V0 AC, VB=V0 BA and VC=V0 CB. Here, AC, CB and BA are unit vectors along the edges of the triangle. If the three masses interact gravitationally, then the magnitude of the net angular momentum of the system at the point of collision is :

  1. 12 a mV0
  2. 3 a mV0
  3. 32 a mV0
  4. 32 a mV0
Ques. 5JEE Main 2025, 28 January (Morning Shift)

The center of mass of a thin rectangular plate (fig - x) with sides of length a and b, whose mass per unit area ( ) varies as = 0 xab (where 0 is a constant), would be . [figure]

  1. ( 23a, 23b )
  2. ( 23a, b2 )
  3. ( 13a, b2 )
  4. ( a2, b2 )
Ques. 6JEE Main 2025, 28 January (Morning Shift)

Two iron solid discs of negligible thickness have radii R1 and R2 and moment of inertia I1 and I2, respectively. For R2 = 2R1, the ratio of I1 and I2 would be 1/x, where x = .

Ques. 7JEE Main 2025, 28 January (Morning Shift)

The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of inertia of a ring rotating in similar way. The moment of inertia of a solid sphere which has same radius as the disc and rotating in similar way, is n times higher than the moment of inertia of the given ring. Here, n = . Consider all the bodies have equal masses.

Ques. 8JEE Main 2025, 28 January (Evening Shift)

A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, is

  1. 290 g
  2. 200 g
  3. 190 g
  4. 300 g
Ques. 9JEE Main 2025, 24 January (Morning Shift)

An object of mass 'm' is projected from origin in a vertical xy plane at an angle 45 with the x-axis with an initial velocity v0. The magnitude and direction of the angular momentum of the object with respect to origin, when it reaches at the maximum height, will be [ g is acceleration due to gravity]

  1. mv032 2 g along negative z-axis
  2. mv032 2 g along positive z-axis
  3. mv034 2 g along positive z-axis
  4. mv034 2 g along negative z-axis
Ques. 10JEE Main 2025, 24 January (Morning Shift)

A uniform solid cylinder of mass 'm' and radius 'r' rolls along an inclined rough plane of inclination 45 . If it starts to roll from rest from the top of the plane then the linear acceleration of the cylinder's axis will be

  1. 2 g
  2. 1 2 g
  3. 13 2 g
  4. 2 g3
Ques. 11JEE Main 2025, 24 January (Evening Shift)

A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be t1 and t2, respectively, then

  1. t1 < t2
  2. t1 = 2t2
  3. t1 > t2
  4. t1 = t2

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