JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Rotational Mechanics

WhatsApp Email

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 '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}

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)A is correct but R is not correct.
(B)Both A and B are correct and R is the correct explanation of A.
(C)Both A and R are correct but R is NOT the correct explanation of A.
(D)A is not correct but R is correct.✓ Correct

Answer: (D)

Solution

For a disc of mass

M

and radius

R

the two diameters give

I_{x} = I_{y} = \frac{M R ^{2}}{4}

, so

k_{x} = k_{y} = \frac{R}{2}

, while the perpendicular axis gives

I_{z} = \frac{M R ^{2}}{2}

and

k_{z} = \frac{R}{2}

. The three radii of gyration are not all equal, so the assertion fails. A rigid body does keep a fixed mass and a fixed shape while it rotates, so the reason is a true statement by itself, but a fixed mass and shape say nothing about how the mass is spread about different axes. Assertion A is not correct but Reason R is correct.

JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Single correct option

Practise more: all JEE Main PYQs on Rotational Mechanics →

JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Rotational Mechanics

Solution

More JEE Main questions on Rotational Mechanics