MHT CET 2024 3rd May Evening Shift | Gravitation Question 27 | Physics

Two identical metal spheres are kept in contact with each other, each having radius ' $R$ ' cm and ' $\rho$ ' is the density of material of metal spheres. The gravitational force ' $F$ ' of attraction between them is proportional to

$\mathrm{R}^3 \rho$

$R^4 \rho^2$

$R^4 \rho$

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

MHT CET 2024 3rd May Morning Shift

MCQ (Single Correct Answer)

-0

The distance of the two planets A and B from the sun are $r_A$ and $r_B$ respectively. Also $r_B$ is equal to $100 r_A$. If the orbital speed of the planet $A$ is ' $v$ ' then the orbital speed of the planet B is

$\frac{\mathrm{v}}{10}$

$\frac{v}{2}$

$ \sqrt{2} v$

10 v

MHT CET 2024 3rd May Morning Shift

MCQ (Single Correct Answer)

-0

Earth has mass ' $M_1$ ' radius ' $R_1$ ' and for moon mass ' $M_2$ ' and radius ' $R_2$ '. Distance between their centres is ' $r$ '. A body of mass ' $M$ ' is placed on the line joining them at a distance $\frac{\mathrm{r}}{3}$ from the centre of the earth. To project a mass ' $M$ ' to escape to infinity, the minimum speed required is

$\left[\frac{2 G}{r}\left(M_2+\frac{M_1}{2}\right)\right]^{1 / 2}$

$\left[\frac{4 \mathrm{G}}{\mathrm{r}}\left(\mathrm{M}_1+\frac{\mathrm{M}_2}{2}\right)\right]^{1 / 2}$

$\left[\frac{3 G}{r}\left(M_1+M_2\right)\right]^{1 / 2}$

$\left[\frac{6 G}{r}\left(M_1+\frac{M_2}{2}\right)\right]^{1 / 2}$

MHT CET 2024 2nd May Evening Shift

MCQ (Single Correct Answer)

-0

The gravitational potential energy required to raise a satellite of mass ' $m$ ' to height ' $h$ ' above the earth's surface is ' $\mathrm{E}_1$ '. Let the energy required to put this satellite into the orbit at the same height be ' $E_2$ '. If $M$ and $R$ are the mass and radius of the earth respectively then $E_1: E_2$ is

$\mathrm{h}: \mathrm{R}$

$\mathrm{h}: 2 \mathrm{R}$

$\mathrm{R}: \mathrm{h}$

$2 \mathrm{~h}: \mathrm{R}$

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