1
JEE Main 2019 (Online) 9th April Evening Slot
+4
-1
A test particle is moving in a circular orbit in the gravitational field produced by a mass density $$\rho (r) = {K \over {{r^2}}}$$ . Identify the correct relation between the radius R of the particle's orbit and its period T
A
T2/R3 is a constant
B
TR is a constant
C
T/R2 is a constant
D
T/R is a constant
2
JEE Main 2019 (Online) 9th April Morning Slot
+4
-1
A solid sphere of mass 'M' and radius 'a' is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M. The gravitational field at distance '3a' from the centre will be :
A
$${{GM} \over {3{a^2}}}$$
B
$${{2GM} \over {9{a^2}}}$$
C
$${{GM} \over {9{a^2}}}$$
D
$${{2GM} \over {3{a^2}}}$$
3
JEE Main 2019 (Online) 8th April Evening Slot
+4
-1
A rocket has to be launched from earth in such a way that it never returns. If E is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have if the same rocket is to be launched from the surface of the moon ? Assume that the density of the earth and the moon are equal and that the earth's volume is 64 times the volume of the moon :-
A
E/32
B
E/16
C
E/4
D
E/64
4
JEE Main 2019 (Online) 8th April Morning Slot
+4
-1
Four identical particles of mass M are located at the corners of a square of side 'a'. What should be their speed if each of them revolves under the influence of other's gravitational field in a circular orbit circumscribing the square?
A
$$1.21\sqrt {{{GM} \over a}}$$
B
$$1.16\sqrt {{{GM} \over a}}$$
C
$$1.41\sqrt {{{GM} \over a}}$$
D
$$1.35\sqrt {{{GM} \over a}}$$
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