1
JEE Main 2021 (Online) 27th August Evening Shift
+4
-1
Two discs have moments of inertia I1 and I2 about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, $$\omega$$1 and $$\omega$$2 respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in kinetic energy of the system in the process is given by :
A
$${{{I_1}{I_2}} \over {({I_1} + {I_2})}}{({\omega _1} - {\omega _2})^2}$$
B
$${{{{({I_1} - {I_2})}^2}{\omega _1}{\omega _2}} \over {2({I_1} + {I_2})}}$$
C
$${{{I_1}{I_2}} \over {2({I_1} + {I_2})}}{({\omega _1} - {\omega _2})^2}$$
D
$${{{{({\omega _1} - {\omega _2})}^2}} \over {2({I_1} + {I_2})}}$$
2
JEE Main 2021 (Online) 27th August Morning Shift
+4
-1
Moment of inertia of a square plate of side l about the axis passing through one of the corner and perpendicular to the plane of square plate is given by :
A
$${{M{l^2}} \over 6}$$
B
$${M{l^2}}$$
C
$${{M{l^2}} \over {12}}$$
D
$${2 \over 3}M{l^2}$$
3
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
4
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)
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