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

Option 1 - <p>15 kgm<sup>2</sup></p>
Option 2 - <p>20/3 kgm<sup>2</sup></p>
Option 3 - <p>20 kgm<sup>2</sup></p>
Option 4 - <p>40/3 kgm<sup>2</sup></p>
1 Views|Posted 4 months ago
Asked by Shiksha User
1 Answer
A
4 months ago
Correct Option - 4
Detailed Solution:

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

 

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I = I 1 + I 2 + I 3

I 1 = m l 2 3

I 2 = m l 2 1 2 + 5 m l 2 4 = I 3

I = m l 2 3 + 2 [ m l 2 1 2 + 5 m l 2 4 ]

= m l 2 3 + 2 × 1 1 2 ( 1 6 ) m l 2

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= 9 3 m l 2 = 3 m l 2

According to question, we can write

l = 2 π r r = l 2 π

I 1 = m l 2 3 , a n d I 2 = m r 2 2 = m l 2 8 π 2

I 1 I 2 = m l 2 3 × 8 π 2 m l 2 = 8 π 2 3

According to question, we can write

l = 2 π r r = l 2 π  

I 1 = m l 2 3 , a n d I 2 = m r 2 2 = m l 2 8 π 2

I 1 I 2 = m l 2 3 × 8 π 2 m l 2 = 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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