1
JEE Main 2023 (Online) 11th April Evening Shift
+4
-1

A space ship of mass $$2 \times 10^{4} \mathrm{~kg}$$ is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the space ship in the orbit to overcome the gravitational pull will be (if $$g=10 \mathrm{~m} / \mathrm{s}^{2}$$ and radius of earth $$=6400 \mathrm{~km}$$ ):

A
$$7.9(\sqrt{2}-1) \mathrm{km} / \mathrm{s}$$
B
$$11.2(\sqrt{2}-1) \mathrm{km} / \mathrm{s}$$
C
$$7.4(\sqrt{2}-1) \mathrm{km} / \mathrm{s}$$
D
$$8(\sqrt{2}-1) \mathrm{km} / \mathrm{s}$$
2
JEE Main 2023 (Online) 11th April Evening Shift
+4
-1

If $$\mathrm{V}$$ is the gravitational potential due to sphere of uniform density on it's surface, then it's value at the center of sphere will be:-

A
$$\frac{3 \mathrm{~V}}{2}$$
B
$$\frac{\mathrm{V}}{2}$$
C
$$\frac{4}{3} \mathrm{~V}$$
D
$$\mathrm{V}$$
3
JEE Main 2023 (Online) 11th April Morning Shift
+4
-1

The radii of two planets 'A' and 'B' are 'R' and '4R' and their densities are $$\rho$$ and $$\rho / 3$$ respectively. The ratio of acceleration due to gravity at their surfaces $$\left(g_{A}: g_{B}\right)$$ will be:

A
3 : 16
B
4 : 3
C
1 : 16
D
3 : 4
4
JEE Main 2023 (Online) 10th April Evening Shift
+4
-1

The time period of a satellite, revolving above earth's surface at a height equal to $$\mathrm{R}$$ will be

(Given $$g=\pi^{2} \mathrm{~m} / \mathrm{s}^{2}, \mathrm{R}=$$ radius of earth)

A
$$\sqrt{32 R}$$
B
$$\sqrt{4 \mathrm{R}}$$
C
$$\sqrt{8 R}$$
D
$$\sqrt{2 R}$$
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