1
JEE Main 2021 (Online) 1st September Evening Shift
+4
-1
Four particles each of mass M, move along a circle of radius R under the action of their mutual gravitational attraction as shown in figure. The speed of each particle is :

A
$${1 \over 2}\sqrt {{{GM} \over {R(2\sqrt 2 + 1)}}}$$
B
$${1 \over 2}\sqrt {{{GM} \over R}(2\sqrt 2 + 1)}$$
C
$${1 \over 2}\sqrt {{{GM} \over R}(2\sqrt 2 - 1)}$$
D
$$\sqrt {{{GM} \over R}}$$
2
JEE Main 2021 (Online) 31st August Evening Shift
+4
-1
If RE be the radius of Earth, then the ratio between the acceleration due to gravity at a depth 'r' below and a height 'r' above the earth surface is : (Given : r < RE)
A
$$1 - {r \over {{R_E}}} - {{{r^2}} \over {R_E^2}} - {{{r^3}} \over {R_E^3}}$$
B
$$1 + {r \over {{R_E}}} + {{{r^2}} \over {R_E^2}} + {{{r^3}} \over {R_E^3}}$$
C
$$1 + {r \over {{R_E}}} - {{{r^2}} \over {R_E^2}} + {{{r^3}} \over {R_E^3}}$$
D
$$1 + {r \over {{R_E}}} - {{{r^2}} \over {R_E^2}} - {{{r^3}} \over {R_E^3}}$$
3
JEE Main 2021 (Online) 31st August Morning Shift
+4
-1
The masses and radii of the earth and moon are (M1, R1) and (M2, R2) respectively. Their centres are at a distance 'r' apart. Find the minimum escape velocity for a particle of mass 'm' to be projected from the middle of these two masses :
A
$$V = {1 \over 2}\sqrt {{{4G({M_1} + {M_2})} \over r}}$$
B
$$V = \sqrt {{{4G({M_1} + {M_2})} \over r}}$$
C
$$V = {1 \over 2}\sqrt {{{2G({M_1} + {M_2})} \over r}}$$
D
$$V = {{\sqrt {2G} ({M_1} + {M_2})} \over r}$$
4
JEE Main 2021 (Online) 27th August Evening Shift
+4
-1
A mass of 50 kg is placed at the centre of a uniform spherical shell of mass 100 kg and radius 50 m. If the gravitational potential at a point, 25 m from the centre is V kg/m. The value of V is :
A
$$-$$60 G
B
+2 G
C
$$-$$20 G
D
$$-$$4 G
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