MHT CET 2024 10th May Evening Shift | Gravitation Question 29 | Physics

A body starts from rest from a distance $\mathrm{R}_0$ from the centre of the earth. The velocity acquired by the body when it reaches the surface of the earth will be ( $R=$ radius of earth, $M=$ mass of earth)

$2 \mathrm{GM}\left(\frac{1}{\mathrm{R}}-\frac{1}{\mathrm{R}_0}\right)$

$\sqrt{2 \mathrm{GM}\left(\frac{1}{\mathrm{R}}-\frac{1}{\mathrm{R}_0}\right)}$

$\mathrm{GM}\left(\frac{1}{\mathrm{R}}-\frac{1}{\mathrm{R}_0}\right)$

$2 \mathrm{GM} \sqrt{\left(\frac{1}{\mathrm{R}}-\frac{1}{\mathrm{R}_0}\right)}$

MHT CET 2024 10th May Morning Shift

MCQ (Single Correct Answer)

-0

The radius and mean density of the planet are four times as that of the earth. The ratio of escape velocity at the earth to the escape velocity at a planet is

$1: \sqrt{8}$

$1: 8$

$1: \sqrt{3}$

$1: 3$

MHT CET 2024 10th May Morning Shift

MCQ (Single Correct Answer)

-0

A small planet is revolving around a very massive star in a circular orbit of radius ' $R$ ' with a period of revolution ' $T$ '. If the gravitational force between the planet and the star were proportional to '$R^{-5 / 2}$', then '$T$' would be proportional to

$\mathrm{R}^{3 / 2}$

$\mathrm{R}^{3 / 5}$

$\mathrm{R}^{7 / 2}$

$\mathrm{R}^{7 / 4}$

MHT CET 2024 9th May Evening Shift

MCQ (Single Correct Answer)

-0

A satellite is revolving around a planet in a circular orbit close to its surface. Let ' $\rho$ ' be the mean density and ' $R$ ' be the radius of the planet. Then the period of the satellite is ( $\mathrm{G}=$ universal constant of gravitation)

$\sqrt{\frac{4 \pi}{\rho G}}$

$\sqrt{\frac{\pi}{\rho G}}$

$\sqrt{\frac{3 \pi}{\rho G}}$

$\sqrt{\frac{2 \pi}{\rho G}}$

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