1
JEE Main 2020 (Online) 4th September Morning Slot
+4
-1
On the x-axis and at a distance x from the origin, the gravitational field due a mass distribution is given by $${{Ax} \over {{{\left( {{x^2} + {a^2}} \right)}^{3/2}}}}$$ in the x-direction. The magnitude of gravitational potential on the x-axis at a distance x, taking its value to be zero at infinity, is:
A
$${A{{\left( {{x^2} + {a^2}} \right)}^{3/2}}}$$
B
$${A{{\left( {{x^2} + {a^2}} \right)}^{1/2}}}$$
C
$${A \over {{{\left( {{x^2} + {a^2}} \right)}^{1/2}}}}$$
D
$${A \over {{{\left( {{x^2} + {a^2}} \right)}^{3/2}}}}$$
2
JEE Main 2020 (Online) 3rd September Evening Slot
+4
-1
The mass density of a planet of radius R varies with the distance r from its centre as
$$\rho$$(r) = $${\rho _0}\left( {1 - {{{r^2}} \over {{R^2}}}} \right)$$.
Then the gravitational field is maximum at :
A
$$r = {1 \over {\sqrt 3 }}R$$
B
r = R
C
$$r = \sqrt {{3 \over 4}} R$$
D
$$r = \sqrt {{5 \over 9}} R$$
3
JEE Main 2020 (Online) 3rd September Morning Slot
+4
-1
A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth’s radius Re . By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that it become $$\sqrt {{3 \over 2}}$$ times larger. Due to this the farthest distance from the centre of the earth that the satellite reaches is R. Value of R is :
A
2Re
B
3Re
C
4Re
D
2.5Re
4
JEE Main 2020 (Online) 2nd September Evening Slot
+4
-1
The height ‘h’ at which the weight of a body will be the same as that at the same depth ‘h’ from the surface of the earth is (Radius of the earth is R and effect of the rotation of the earth is neglected)
A
$${R \over 2}$$
B
$${{\sqrt 5 R - R} \over 2}$$
C
$${{\sqrt 3 R - R} \over 2}$$
D
$${{\sqrt 5 } \over 2}R - R$$
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