Given below are two statements : one is labelled as Assertion A a… - Vidyadip

MCQ

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 of mass $'M'$ and radius $'R'$ about $X, Y$ axes (passing through its plane) and $Z-$axis which is perpendicular to its plane were found to be $I_{x}, I_{y}$ and ${I}_{z}$ 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 :

A
Both $A$ and $R$ are correct but $R$ is NOT the correct explanation of $A$.
✓
$A$ is not correct but $R$ is correct.
C
$A$ is correct but $R$ is not correct.
D
Both $A$ and $R$ are correct and $R$ is the correct explanation of $A$.

✓

Answer

Correct option: B.

$A$ is not correct but $R$ is correct.

b
$I_{z}=I_{x}+I_{y}$ (using perpendicular axls theorem)

$l = mk ^{2}$ (K: radius of gyratlon)

so $m K_{z}^{2}=m K_{x}^{2}+m K_{y}^{2}$

$K_{z}^{2}=K_{x}^{2}+K_{y}^{2}$

so radius of gyration about axes $x, y$ and $z$ won't be same hense asseration $A$ is not correct reason $R$ is correct statement (property of a rlgid body)

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