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System of Particles and Rotational Motion · Question 45

JEE Main 2025 (Online) 2nd April Evening ShiftMCQEasy📈 Topic in 32% papers+4−1
1

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)

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2

[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)

JEE Main 2025 (Online) 2nd April Evening Shift
3

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 .

JEE Main 2025 (Online) 29th January Morning Shift
4

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 )
JEE Main 2025 (Online) 28th January Morning Shift
5

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 = .

JEE Main 2025 (Online) 28th January Morning Shift
6

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.

JEE Main 2025 (Online) 28th January Morning Shift
7

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
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