1
JEE Main 2021 (Online) 26th August Evening Shift
+4
-1
The solid cylinder of length 80 cm and mass M has a radius of 20 cm. Calculate the density of the material used if the moment of inertia of the cylinder about an axis CD parallel to AB as shown in figure is 2.7 kg m2.

A
14.9 kg/m3
B
7.5 $$\times$$ 101 kg/m3
C
7.5 $$\times$$ 102 kg/m3
D
1.49 $$\times$$ 102 kg/m3
2
JEE Main 2021 (Online) 27th July Morning Shift
+4
-1
List-I List-II
(a) MI of the rod (length L, Mass M, about an axis $$\bot$$ to the rod passing through the midpoint) (i) $$8M{L^2}/3$$
(b) MI of the rod (length L, Mass 2M, about an axis $$\bot$$ to the rod passing through one of its end) (ii) $$M{L^2}/3$$
(c) MI of the rod (length 2L, Mass M, about an axis $$\bot$$ to the rod passing through its midpoint) (iii) $$M{L^2}/12$$
(d) MI of the rod (Length 2L, Mass 2M, about an axis $$\bot$$ to the rod passing through one of its end) (iv) $$2M{L^2}/3$$

Choose the correct answer from the options given below:
A
(a)-(ii), (b)-(iii), (c)-(i), (d)-(iv)
B
(a)-(ii), (b)-(i), (c)-(iii), (d)-(iv)
C
(a)-(iii), (b)-(iv), (c)-(ii), (d)-(i)
D
(a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
3
JEE Main 2021 (Online) 27th July Morning Shift
+4
-1
The figure shows two solid discs with radius R and r respectively. If mass per unit area is same for both, what is the ratio of MI of bigger disc around axis AB (Which is $$\bot$$ to the plane of the disc and passing through its centre) of MI of smaller disc around one of its diameters lying on its plane? Given 'M' is the mass of the larger disc. (MI stands for moment of inertia)

A
R2 : r2
B
2r4 : R4
C
2R2 : r2
D
2R4 : r4
4
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
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 Ix, Iy and Iz respectively. The respectively 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.
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