JEE Main 2024 (Online) 6th April Morning Shift | Gravitation Question 6 | Physics

To project a body of mass $$m$$ from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is $$R_E, g=$$ acceleration due to gravity on the surface of earth):

$$1 / 2 m g R_E$$

$$4 m g R_E$$

$$m g R_E$$

$$2 m g R_E$$

JEE Main 2024 (Online) 5th April Evening Shift

MCQ (Single Correct Answer)

-1

A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is :

(Given $$=$$ Radius of geo-stationary orbit for earth is $$4.2 \times 10^4 \mathrm{~km}$$)

$$1.68 \times 10^5 \mathrm{~km}$$

$$1.4 \times 10^4 \mathrm{~km}$$

$$8.4 \times 10^4 \mathrm{~km}$$

$$1.05 \times 10^4 \mathrm{~km}$$

JEE Main 2024 (Online) 5th April Morning Shift

MCQ (Single Correct Answer)

-1

If $$\mathrm{G}$$ be the gravitational constant and $$\mathrm{u}$$ be the energy density then which of the following quantity have the dimensions as that of the $$\sqrt{\mathrm{uG}}$$ :

Gravitational potential

pressure gradient per unit mass

Energy per unit mass

Force per unit mass

JEE Main 2024 (Online) 5th April Morning Shift

MCQ (Single Correct Answer)

-1

Match List I with List II :

	LIST I		LIST II
A.	Kinetic energy of planet	I.	$$ -\mathrm{GMm} / \mathrm{a} $$
B.	Gravitation Potential energy of sun-planet system	II.	$$ \mathrm{GMm} / 2 \mathrm{a} $$
C.	Total mechanical energy of planet	III.	$$ \frac{\mathrm{Gm}}{\mathrm{r}} $$
D.	Escape energy at the surface of planet for unit mass object	IV.	$$ -\mathrm{GMm} / 2 \mathrm{a} $$