1
JEE Main 2023 (Online) 1st February Evening Shift
+4
-1

The escape velocities of two planets $$\mathrm{A}$$ and $$\mathrm{B}$$ are in the ratio $$1: 2$$. If the ratio of their radii respectively is $$1: 3$$, then the ratio of acceleration due to gravity of planet A to the acceleration of gravity of planet B will be :

A
$$\frac{4}{3}$$
B
$$\frac{2}{3}$$
C
$$\frac{3}{4}$$
D
$$\frac{3}{2}$$
2
JEE Main 2023 (Online) 1st February Evening Shift
+4
-1

For a body projected at an angle with the horizontal from the ground, choose the correct statement.

A
Gravitational potential energy is maximum at the highest point.
B
The vertical component of momentum is maximum at the highest point.
C
The horizontal component of velocity is zero at the highest point.
D
The Kinetic Energy (K.E.) is zero at the highest point of projectile motion.
3
JEE Main 2023 (Online) 1st February Morning Shift
+4
-1

If earth has a mass nine times and radius twice to that of a planet P. Then $$\frac{v_{e}}{3} \sqrt{x} \mathrm{~ms}^{-1}$$ will be the minimum velocity required by a rocket to pull out of gravitational force of $$\mathrm{P}$$, where $$v_{e}$$ is escape velocity on earth. The value of $$x$$ is

A
1
B
3
C
2
D
18
4
JEE Main 2023 (Online) 1st February Morning Shift
+4
-1

Given below are two statements:

Statement I: Acceleration due to gravity is different at different places on the surface of earth.

Statement II: Acceleration due to gravity increases as we go down below the earth's surface.

In the light of the above statements, choose the correct answer from the options given below

A
Both Statement I and Statement II are true
B
Both Statement I and Statement II are false
C
Statement I is false but Statement II is true
D
Statement I is true but Statement II is false
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