1
JEE Main 2024 (Online) 9th April Morning Shift
+4
-1

An astronaut takes a ball of mass $$m$$ from earth to space. He throws the ball into a circular orbit about earth at an altitude of $$318.5 \mathrm{~km}$$. From earth's surface to the orbit, the change in total mechanical energy of the ball is $$x \frac{\mathrm{GM}_{\mathrm{e}} \mathrm{m}}{21 \mathrm{R}_{\mathrm{e}}}$$. The value of $$x$$ is (take $$\mathrm{R}_{\mathrm{e}}=6370 \mathrm{~km})$$ :

A
12
B
11
C
9
D
10
2
JEE Main 2024 (Online) 8th April Evening Shift
+4
-1

Two satellite A and B go round a planet in circular orbits having radii 4R and R respectively. If the speed of $$\mathrm{A}$$ is $$3 v$$, the speed of $$\mathrm{B}$$ will be :

A
$$6 v$$
B
$$\frac{4}{3} v$$
C
$$3 v$$
D
$$12 v$$
3
JEE Main 2024 (Online) 8th April Morning Shift
+4
-1

Two planets $$A$$ and $$B$$ having masses $$m_1$$ and $$m_2$$ move around the sun in circular orbits of $$r_1$$ and $$r_2$$ radii respectively. If angular momentum of $$A$$ is $$L$$ and that of $$B$$ is $$3 \mathrm{~L}$$, the ratio of time period $$\left(\frac{T_A}{T_B}\right)$$ is:

A
$$\left(\frac{r_2}{r_1}\right)^{\frac{3}{2}}$$
B
$$27\left(\frac{m_1}{m_2}\right)^3$$
C
$$\left(\frac{r_1}{r_2}\right)^3$$
D
$$\frac{1}{27}\left(\frac{m_2}{m_1}\right)^3$$
4
JEE Main 2024 (Online) 6th April Evening Shift
+4
-1

Assuming the earth to be a sphere of uniform mass density, a body weighed $$300 \mathrm{~N}$$ on the surface of earth. How much it would weigh at R/4 depth under surface of earth ?

A
75 N
B
375 N
C
300 N
D
225 N
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