1
JEE Main 2023 (Online) 15th April Morning Shift
+4
-1
Two identical particles each of mass ' $m$ ' go round a circle of radius $a$ under the action of their mutual gravitational attraction. The angular speed of each particle will be :
A
$\sqrt{\frac{G m}{2 a^{3}}}$
B
$\sqrt{\frac{G m}{a^{3}}}$
C
$\sqrt{\frac{G m}{8 a^{3}}}$
D
$\sqrt{\frac{G m}{4 a^{3}}}$
2
JEE Main 2023 (Online) 15th April Morning Shift
+4
-1
A body is released from a height equal to the radius $(\mathrm{R})$ of the earth. The velocity of the body when it strikes the surface of the earth will be

(Given $g=$ acceleration due to gravity on the earth.)
A
$\sqrt{\frac{g R}{2}}$
B
$\sqrt{4 g R}$
C
$\sqrt{2 g R}$
D
$\sqrt{g R}$
3
JEE Main 2023 (Online) 13th April Evening Shift
+4
-1

Given below are two statements:

Statement I : For a planet, if the ratio of mass of the planet to its radius increases, the escape velocity from the planet also increases.

Statement II : Escape velocity is independent of the radius of the planet.

In the light of above statements, choose the most appropriate answer form the options given below

A
Both Statement I and Statement II are correct
B
Statement I is correct but statement II is incorrect
C
Both Statement I and Statement II are incorrect
D
Statement I is incorrect but statement II is correct
4
JEE Main 2023 (Online) 13th April Evening Shift
+4
-1

Two planets A and B of radii $$\mathrm{R}$$ and 1.5 R have densities $$\rho$$ and $$\rho / 2$$ respectively. The ratio of acceleration due to gravity at the surface of $$\mathrm{B}$$ to $$\mathrm{A}$$ is:

A
2 : 1
B
2 : 3
C
4 : 3
D
3 : 4
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