SATHEE: Rotational Motion Question 130

Rotational Motion Question 130

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

Options:

A) $I_{Y} = 64 I_{X}$

B) $I_{Y} = 32 I_{X}$

C) $I_{Y} = 16 I_{X}$

D) $I_{Y} = I_{X}$

Show Answer

Answer:

Correct Answer: A

Solution:

[a]Moment of Inertia of disc $

$I = \frac{1}{2} M R^{2}$

$= \frac{1}{2} (π R^{2} t ρ) R^{2} = \frac{1}{2} π t ρ R^{4}$

As M= $V \times ρ = π R^{2} t ρ$

$w h e r e t = t h i c k n e s s, ρ = d e n s i t y$

$∴ \frac{I_{y}}{I_{x}} = \frac{t_{y}}{t_{x}} {(\frac{R_{y}}{R_{x}})}^{4}$

$i f ρ = c o n s t a n t$

$\Rightarrow \frac{I_{y}}{I_{x}} = \frac{1}{4} {(4)}^{4} = 64$

Given $R_{y} = 4 R_{x}, t_{y} = \frac{t_{x}}{4}$

$\Rightarrow I_{y} = 64 I_{x}$

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Rotational Motion Question 130

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 IxandIY is

Options:

Answer:

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 4 $R$ is made from an iron plate of thickness $t$ /4. Then the relation between the moment of inertia $I_{x} a n d I_{Y}$ is