1
JEE Main 2021 (Online) 26th February Morning Shift
MCQ (Single Correct Answer)
+4
-1
Four identical solid spheres each of mass 'm' and radius 'a' are placed with their centres on the four corners of a square of side 'b'. The moment of inertia of the system about one side of square where the axis of rotation is parallel to the plane of the square is :
A
$${4 \over 5}m{a^2}$$
B
$${8 \over 5}m{a^2} + m{b^2}$$
C
$${4 \over 5}m{a^2} + 2m{b^2}$$
D
$${8 \over 5}m{a^2} + 2m{b^2}$$
2
JEE Main 2021 (Online) 25th February Evening Shift
MCQ (Single Correct Answer)
+4
-1
A sphere of radius 'a' and mass 'm' rolls along a horizontal plane with constant speed v0. It encounters an inclined plane at angle $$\theta$$ and climbs upward. Assuming that it rolls without slipping, how far up the sphere will travel?

A
$${{v_0^2} \over {2g\sin \theta }}$$
B
$${{7v_0^2} \over {10g\sin \theta }}$$
C
$${2 \over 5}{{v_0^2} \over {g\sin \theta }}$$
D
$${{v_0^2} \over {5g\sin \theta }}$$
3
JEE Main 2021 (Online) 24th February Morning Shift
MCQ (Single Correct Answer)
+4
-1
Moment of inertia (M. I.) of four bodies, having same mass and radius, are reported as;

I1 = M.I. of thin circular ring about its diameter,

I2 = M.I. of circular disc about an axis perpendicular to disc and going through the centre,

I3 = M.I. of solid cylinder about its axis and

I4 = M.I. of solid sphere about its diameter.

Then :
A
I1 = I2 = I3 > I4
B
I1 + I3 < I2 + I4
C
I1 = I2 = I3 < I4
D
I1 + I2 = I3 + $${5 \over 2}$$ I4
4
JEE Main 2020 (Online) 6th September Evening Slot
MCQ (Single Correct Answer)
+4
-1
The linear mass density of a thin rod AB of length L varies from A to B as
$$\lambda \left( x \right) = {\lambda _0}\left( {1 + {x \over L}} \right)$$, where x is the distance from A. If M is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular to the rod is :
A
$${2 \over 5}M{L^2}$$
B
$${5 \over {12}}M{L^2}$$
C
$${7 \over {18}}M{L^2}$$
D
$${3 \over 7}M{L^2}$$
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