1
JEE Main 2021 (Online) 26th February Morning Shift
+4
-1
Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance (R/2) from the earth's centre, where 'R' is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period :
A
$$2\pi \sqrt {{R \over g}}$$
B
$${g \over {2\pi R}}$$
C
$${{2\pi R} \over g}$$
D
$${1 \over {2\pi }}\sqrt {{g \over R}}$$
2
JEE Main 2021 (Online) 26th February Morning Shift
+4
-1
A planet revolving in elliptical orbit has :

A. a constant velocity of revolution.

B. has the least velocity when it is nearest to the sun.

C. its areal velocity is directly proportional to its velocity.

D. areal velocity is inversely proportional to its velocity.

E. to follow a trajectory such that the areal velocity is constant.

Choose the correct answer from the options given below :
A
D only
B
E only
C
C only
D
A only
3
JEE Main 2021 (Online) 26th February Morning Shift
+4
-1
Find the gravitational force of attraction between the ring and sphere as shown in the diagram, where the plane of the ring is perpendicular to the line joining the centres. If $$\sqrt 8$$R is the distance between the centres of a ring (of mass 'm') and a sphere (mass 'M') where both have equal radius 'R'.

A
$${{2\sqrt 2 } \over 3}.{{GMm} \over {{R^2}}}$$
B
$${{\sqrt 8 } \over 9}.{{GmM} \over R}$$
C
$${{\sqrt 8 } \over {27}}.{{GmM} \over {{R^2}}}$$
D
$${1 \over {3\sqrt 8 }}.{{GMm} \over {{R^2}}}$$
4
JEE Main 2021 (Online) 25th February Morning Slot
+4
-1
A solid sphere of radius R gravitationally attracts a particle placed at 3R from its centre with a force F1. Now a spherical cavity of radius $$\left( {{R \over 2}} \right)$$ is made in the sphere (as shown in figure) and the force becomes F2. The value of F1 : F2 is

A
36 : 25
B
41 : 50
C
50 : 41
D
25 : 36
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