JEE Main Gravitation Practice Questions With Solutions

A satellite of ${10}^3\mathrm{kg}$10^{3} \textrm{ } kg mass is revolving in circular orbit of radius $2R$2 R. If $\frac{{10}^{4}R}{6}\mathrm{J}$\frac{10^{4} R}{6} \textrm{ } J energy is supplied to the satellite, it would revolve in a new circular orbit of radius

(use $g=10\mathrm{m}/{\mathrm{s}}^2,R=$g = 10 \textrm{ } m / s^{2} , R = radius of earth)

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

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

Two planets $A$A and $B$B having masses $m_1$m_{1} and $m_2$m_{2} move around the sun in circular orbits of $r_1$r_{1} and $r_2$r_{2} radii respectively. If angular momentum of $A$A is $L$L and that of $B$B is $3\mathrm{L}$3 \textrm{ } L, the ratio of time period $\left(\frac{T_A}{T_B}\right)$\left(\right. \frac{T_{A}}{T_{B}} \left.\right) is:

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

To project a body of mass $m$m from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is $R_E,g=$R_{E} , g = acceleration due to gravity on the surface of earth):

A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is :

(Given $=$= Radius of geo-stationary orbit for earth is $4.2\times {10}^4\mathrm{km}$4.2 \times 10^{4} \textrm{ } km)

If $\mathrm{G}$G be the gravitational constant and $\mathrm{u}$u be the energy density then which of the following quantity have the dimensions as that of the $\sqrt{\mathrm{uG}}$\sqrt{uG} :

Match List I with List II :

(Where $\mathrm{a}=$a = radius of planet orbit, $\mathrm{r}=$r = radius of planet, $\mathrm{M}=$M = mass of Sun, $\mathrm{m}=$m = mass of planet)

Choose the correct answer from the options given below :

A $90\mathrm{kg}$90 \textrm{ } kg body placed at $2\mathrm{R}$2 R distance from surface of earth experiences gravitational pull of :

($\mathrm{R}=$R = Radius of earth, $\mathrm{g}=10\mathrm{m}{\mathrm{s}}^{-2}$g = 10 \textrm{ } m \left(\textrm{ } s\right)^{- 2})