1
JEE Main 2023 (Online) 29th January Morning Shift
+4
-1

Two particles of equal mass '$$m$$' move in a circle of radius '$$r$$' under the action of their mutual gravitational attraction. The speed of each particle will be :

A
$$\sqrt{\frac{G m}{4 r}}$$
B
$$\sqrt{\frac{G m}{2 r}}$$
C
$$\sqrt{\frac{G m}{r}}$$
D
$$\sqrt{\frac{4 G m}{r}}$$
2
JEE Main 2023 (Online) 25th January Evening Shift
+4
-1

Every planet revolves around the sun in an elliptical orbit :-

A. The force acting on a planet is inversely proportional to square of distance from sun.

B. Force acting on planet is inversely proportional to product of the masses of the planet and the sun.

C. The Centripetal force acting on the planet is directed away from the sun.

D. The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit.

Choose the correct answer from the options given below :

A
C and D only
B
B and C only
C
A and D only
D
A and C only
3
JEE Main 2023 (Online) 25th January Evening Shift
+4
-1

A body of mass is taken from earth surface to the height h equal to twice the radius of earth (R$$_e$$), the increase in potential energy will be :

(g = acceleration due to gravity on the surface of Earth)

A
$$\frac{1}{2}mgR_e$$
B
$$3~mgR_e$$
C
$$\frac{1}{3}mgR_e$$
D
$$\frac{2}{3}mgR_e$$
4
JEE Main 2023 (Online) 25th January Morning Shift
+4
-1

Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is 100 g. The time period of the motion of the particle will be (approximately)

(Take g = 10 m s$$^{-2}$$ , radius of earth = 6400 km)

A
12 hours
B
1 hour 24 minutes
C
24 hours
D
1 hour 40 minutes
EXAM MAP
Medical
NEET