1
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
$$V = {{\sqrt {2G} ({M_1} + {M_2})} \over r}$$
2
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
3
JEE Main 2021 (Online) 26th August Morning Shift
+4
-1
Inside a uniform spherical shell :

(1) the gravitational field is zero

(2) the gravitational potential is zero

(3) the gravitational field is same everywhere

(4) the gravitational potential is same everywhere

(5) all of the above

Choose the most appropriate answer from the options given below :
A
(1), (3) and (4) only
B
(5) only
C
(1), (2) and (3) only
D
(2), (3) and (4) only
4
JEE Main 2021 (Online) 27th July Evening Shift
+4
-1
Two identical particles of mass 1 kg each go round a circle of radius R, under the action of their mutual gravitational attraction. The angular speed of each particle is :
A
$$\sqrt {{G \over {2{R^3}}}}$$
B
$${1 \over 2}\sqrt {{G \over {{R^3}}}}$$
C
$${1 \over {2R}}\sqrt {{1 \over G}}$$
D
$${{2G} \over {{R^3}}}$$
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