1
JEE Main 2021 (Online) 31st August Evening Shift
+4
-1
A system consists of two identical spheres each of mass 1.5 kg and radius 50 cm at the end of light rod. The distance between the centres of the two spheres is 5 m. What will be the moment of inertia of the system about an axis perpendicular to the rod passing through its midpoint?
A
18.75 kgm2
B
1.905 $$\times$$ 105 kgm2
C
19.05 kgm2
D
1.875 $$\times$$ 105 kgm2
2
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
$${{{{({\omega _1} - {\omega _2})}^2}} \over {2({I_1} + {I_2})}}$$
3
JEE Main 2021 (Online) 27th August Morning Shift
+4
-1
A huge circular arc of length 4.4 ly subtends an angle '4s' at the centre of the circle. How long it would take for a body to complete 4 revolution if its speed is 8 AU per second?

Given : 1 ly = 9.46 $$\times$$ 1015 m

1 AU = 1.5 $$\times$$ 1011 m
A
4.1 $$\times$$ 108 s
B
4.5 $$\times$$ 1010 s
C
3.5 $$\times$$ 106 s
D
7.2 $$\times$$ 108 s
4
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
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