1
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

A satellite is orbiting just above the surface of the planet of density ' $\rho$ ' with periodic time ' $T$ '. The quantity $\mathrm{T}^2 \rho$ is equal to ( $\mathrm{G}=$ universal gravitational constant)

A
$\frac{4 \pi^2}{G}$
B
$\frac{3 \pi^2}{G}$
C
$\frac{3 \pi}{G}$
D
$\frac{\pi}{G}$
2
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

The speed with which the earth would have to rotate about its axis so that a person on the equator would weigh $\frac{3}{5}$ th as much as at present weight is ( $\mathrm{g}=$ gravitational acceleration, $\mathrm{R}=$ equatorial radius of the earth)

A
$\sqrt{\frac{2 g}{5 R}}$
B
$\sqrt{\frac{3 \mathrm{~g}}{5 \mathrm{R}}}$
C
$\sqrt{\frac{5 R}{3 g}}$
D
$\sqrt{\frac{3}{5}} \mathrm{gR}$
3
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

A simple pendulum has a periodic time ' $\mathrm{T}_1$ ' when it is on the surface of earth of radius ' $R$ '. Its periodic time is ' $\mathrm{T}_2$ ' when it is taken to a height ' $R$ ' above the earth's surface. The value of $\frac{T_2}{T_1}$ is

A
$\sqrt2$
B
1
C
2
D
$\frac{1}{2}$
4
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

The minimum energy required to launch a satellite of mass $m$ from the surface of a planet of mass $M$ and radius $R$ in a circular orbit at an altitude of $2 R$ is

A
$\frac{5 \mathrm{GMm}}{6 \mathrm{R}}$
B
$\frac{2 \mathrm{GMm}}{3 \mathrm{R}}$
C
$\frac{\mathrm{GMm}}{2 \mathrm{R}}$
D
$\frac{\mathrm{GMm}}{3 \mathrm{R}}$
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