JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
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 \(A\).
- B \(A\) 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 & Solution
Correct Answer
(B) \(A\) is not correct but \(R\) is correct.
Step-by-step Solution
Detailed explanation
\(I_{z}=I_{x}+I_{y}\) (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…
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