SATHEE: Rotational Motion Question 6

Rotational Motion Question 6

Question: A circular disc X of radius R is made from an iron plate of thickness t and another disc Y of radius 4R is made from an iron plate of thickness t/4. Then, the relation between the moment of inertia $I_{X}$ and $I_{Y}$ is

[AIEEE 2003]

Options:

A) $l_{Y} = 32 l_{X}$

B) $l_{Y} = 16 l_{X}$

C) $l_{Y} = l_{X}$

D) $l_{Y} = 64 l_{X}$

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Answer:

Correct Answer: D

Solution:

Mass of disc (X), $m_{x} = π R^{2} t ρ$ $(m = v ρ = A t ρ = π R^{2} - ρ)$

where, $ρ =$ density of material of disc

$∴$ $l_{x} = \frac{1}{2} m_{x} R^{2} = \frac{1}{2} π R^{2} t ρ R^{2}$ $l_{x} = \frac{1}{2} π ρ t R^{4}$ …

(i) Mass of disc (Y) $m_{Y} = π {(4 R)}^{2} \frac{t}{4} ρ = 4 π R^{2} t ρ$

and $l_{Y} = \frac{1}{2} m_{Y} {(4 R)}^{2} = \frac{1}{2} 4 R^{2} t ρ .16 R^{2}$

$\Rightarrow$ $l_{Y} = 32 π t ρ R^{4}$ …(ii)

$∴$ $\frac{l_{Y}}{l_{X}} = \frac{32 π t ρ R^{4}}{\frac{1}{2} π ρ t R^{4}} = 64$

$∴$ $l_{Y} = 64 l_{X}$

Rotational Motion Question 6

Question: A circular disc X of radius R is made from an iron plate of thickness t and another disc Y of radius 4R is made from an iron plate of thickness t/4. Then, the relation between the moment of inertia $I_{X}$ and $I_{Y}$ is

Options:

Answer:

Solution:

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Rotational Motion Question 6

Question: A circular disc X of radius R is made from an iron plate of thickness t and another disc Y of radius 4R is made from an iron plate of thickness t/4. Then, the relation between the moment of inertia IX and IY is

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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Question: A circular disc X of radius R is made from an iron plate of thickness t and another disc Y of radius 4R is made from an iron plate of thickness t/4. Then, the relation between the moment of inertia $I_{X}$ and $I_{Y}$ is