1
JEE Main 2020 (Online) 8th January Morning Slot
+4
-1
Consider two solid spheres of radii R1 = 1m, R2 = 2m and masses M1 and M2, respectively. The gravitational field due to sphere (1) and (2) are shown. The value of $${{{M_1}} \over {{M_2}}}$$ is :
A
$${2 \over 3}$$
B
$${1 \over 6}$$
C
$${1 \over 2}$$
D
$${1 \over 3}$$
2
JEE Main 2020 (Online) 7th January Evening Slot
+4
-1
A box weight 196 N on a spring balance at the north pole. Its weight recorded on the same balance if it is shifted to the equator is close to (Take g = 10 ms–2 at the north pole and the radius of the earth = 6400 km) :
A
194.32 N
B
195.66 N
C
195.32 N
D
194.66 N
3
JEE Main 2020 (Online) 7th January Morning Slot
+4
-1
A satellite of mass m is launched vertically upwards with an initial speed u from the surface of the earth. After it reaches height R (R = radius of the earth), it ejects a rocket of mass $${m \over {10}}$$ so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is (G is the gravitational constant; M is the mass of the earth) :
A
$${{3m} \over 8}{\left( {u + \sqrt {{{5GM} \over {6R}}} } \right)^2}$$
B
$${m \over {20}}\left( {{u^2} + {{113} \over {100}}{{GM} \over R}} \right)$$
C
$$5m\left( {{u^2} - {{119} \over {100}}{{GM} \over R}} \right)$$
D
$${m \over {20}}{\left( {u - \sqrt {{{2GM} \over {3R}}} } \right)^2}$$
4
JEE Main 2019 (Online) 12th April Evening Slot
+4
-1
The ratio of the weights of a body on the Earth’s surface to that on the surface of a planets is 9 : 4. The mass of the planet is $${1 \over 9}$$ th of that of the Earth. If 'R' is the radius of the Earth, what is the radius of the planet ? (Take the planets to have the same mass density)
A
$${R \over 9}$$
B
$${R \over 2}$$
C
$${R \over 3}$$
D
$${R \over 4}$$
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