1
JEE Main 2021 (Online) 25th February Evening Shift
+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
$${{v_0^2} \over {5g\sin \theta }}$$
2
JEE Main 2021 (Online) 24th February Evening Slot
+4
-1
A circular hole of radius $$\left( {{a \over 2}} \right)$$ is cut out of a circular disc of radius 'a' as shown in figure. The centroid of the remaining circular portion with respect to point 'O' will be :

A
$${1 \over 6}a$$
B
$${2 \over 3}a$$
C
$${5 \over 6}a$$
D
$${10 \over 11}a$$
3
JEE Main 2021 (Online) 24th February Morning Slot
+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
+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
$${3 \over 7}M{L^2}$$
JEE Main Subjects
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
EXAM MAP
Joint Entrance Examination