Class 11th Moment of Inertia Physics System of Particles and Rotational Motion Physics

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Moment of inertia of a circular disc 'M' and radius 'R' about X, Y axes (passing through its plane) and Z-axis which is perpendicular to its plane were found to be I?, I? & I? respectively. The respective radii of gyration about all the three axes will be the same.

Reason R: A rigid body making rotational motion has fixed mass and shape.

In the light of the above statements, choose the most appropriate answer from the options given below:

Option 1 - <p>A is correct but R is not correct.</p>

Option 2 - <p>Both A and R are correct and R is the correct explanation of A.</p>

Option 3 - <p>Both A and R are correct but R is NOT the correct explanation of A.<br><br></p>

Option 4 - <p>A is not correct but R is correct</p>

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Two solid spheres each of mass 2 kg and radius 75 cm are arranged as shown. Find MOI of the system about the given axis.

Alok Kumar Singh

$I = (\frac{2}{5} M R^{2} + M R^{2}) \times 2$

$= \frac{14}{5} \times 2 \times \frac{9}{16}$

$= \frac{63}{20}$

= 3.15 kg m²

Two particles of masses 5 kg and 10 kg are placed along x-axis at positions x = 1 m and x = 3 m. The moment of inertia of the system about an axis respectively passing through centre of mass and parallel to y-axis is

Alok Kumar Singh

Distance of CM from 5 kg = 10*2/15 = 4/3m

Two circular rings (of same material) are of same thickness. The diameter of first ring is twice that of second. The moment of inertia of first ring as compared to that of second is

Alok Kumar Singh

Moment of inertia of a system made from three uniform rods each of mass m and length l joined to each other, as shown in the figure about one end O and perpendicular to its plane will be

The momentum of inertia of a uniform thin rod about a perpendicular axis passing through on end is I1. The same rod is into a ring and its moment of inertia about a diameter is I2. If $\frac{I_{1}}{I_{2}} i s \frac{X π^{2}}{3},$ $\frac{_{}}{_{}} \frac{^{}}{}$ then the value of x will be__________.

According to question, we can write

$l = 2 π r \Rightarrow r = \frac{l}{2 π}$

$I_{1} = \frac{m l^{2}}{3}, a n d I_{2} = \frac{m r^{2}}{2} = \frac{m l^{2}}{8 π^{2}}$

$\Rightarrow \frac{I_{1}}{I_{2}} = \frac{m l^{2}}{3} \times \frac{8 π^{2}}{m l^{2}} = \frac{8 π^{2}}{3}$

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Physics System of Particles and Rotational Motion 2025

Physics System of Particles and Rotational Motion 2025

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