Gravitation

The percentage decrease in the weight of a body when taken to a height of $48$ km above the surface of the earth is (Radius of the earth is $6400$ km)

Select the correct statement out of the following

A geostationary satellite is orbiting the earth at a height of $4R$ above the surface of the earth, where $R$ is the radius of the earth. Another satellite is orbiting the earth at a height $1.5R$ from the surface of the earth with periodic...

A satellite is revolving around a planet in a circular orbit close to its surface. Let $\rho$ be mean density and $R$ be the radius of the planet; then the period of the satellite is($G$ = Universal constant of gravitation).

Time period of a simple pendulum is $T_1$ when on the earth's surface and $T_2$ when taken to a height '2R' above the earth's surface, where 'R' is the radius of the earth. The ratio $T_1 : T_2$ is

The lengths of seconds pendulums on the surface of the earth and at an altitude '$h$' from the surface of the earth are $l_s$ and $l_h$ respectively. The radius of the earth is

The acceleration due to gravity at a height 'h' above the surface of earth is '$g_h$'. At the depth 90 km below the earth's surface the acceleration due to gravity is also '$g_h$'. The value of 'h' is

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

Two planets A and B are orbiting around the sun. The distances of the two planets A and B from the sun are $r_A$ and $r_B$ respectively. Also $r_B = 225\, r_A$. If the orbital speed of the planet A is 'V' then the orbital speed of planet B ...

The masses and radii of the earth and moon are $M_1$, $R_1$ and $M_2$, $R_2$ and respectively, Their centres are at a distance 'd' apart. The minimum speed with which body of mass 'm' should be projected from a distance $2d/3$ from the cent...

The time taken by simple pendulum for one oscillation is T on earth's surface. Its time period becomes xT when taken to a height R (equal to earth's radius) above the earth's surface. The value of x is

A body of mass m is taken from earth surface to a height h equal to twice the radius of earth, the increase in potential energy will be ($g$ = acceleration due to gravity on earth's surface) (R - radius of earth)

What should be the angular velocity of earth due to rotation about its own axis so that the weight at equator becomes $\left(\dfrac{3}{5}\right)^{th}$ of initial value? ($g =$ acceleration due to gravity, R = radius of earth)

The distance of the two planets A and B from the sun are '$r_A$' and '$r_B$' respectively such that $r_B = 100\, r_A$. The ratio of the speed of planet A to that of planet B is (both the planets are revolving around the sun)

A body is projected vertically from earth's surface of radius R with velocity equal to half the escape velocity. The maximum height reached by the body is

If earth has a mass nine times and radius twice to the planet P. Then $\dfrac{v_e}{3}\sqrt{x}$ ms$^{-1}$ will be the minimum velocity required by a rocket to pull out of gravitational force of P, where $v_e$ is escape velocity on earth. The...

Given below are two statements:Statement I: Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface.Statement II: Acceleration due to earth's gravity is same at a height '$h$' and depths '$d$' from earth'...

The density of a planet is three times that of earth and radius $2.5$ times that of earth. If $g_p$ and $g_e$ represents acceleration due to gravity on planet and earth respectively then ratio $g_p$ to $g_e$ is

A uniform sphere has radius ' $R$ ' and mass ' $M$ '. The magnitude of gravitational field at distances ' $\mathrm{r}_1$ ' and ' $\mathrm{r}_2$ ' from the centre of the sphere are ' $E_1$ ' and ' $E_2$ ' respectively. The ratio $E_1: E_2$ i...

A body weighs 45 N on the surface of the earth. The gravitational force on a body due to earth at a height equal to half the radius of earth will be

The depth at which acceleration due to gravity becomes $\frac{g^{\prime}}{n}$ is ( $R=$ radius of earth, $\mathrm{g}=$ acceleration due to gravity) ( $\mathrm{n}=$ integer)

Two planets A and B have densities ' $\rho_1$ ', ' $\rho_2$ ' and have radii ' $r_1$ ', ' $r_2$ ', respectively. The ratio of acceleration due to gravity on $A$ to that of $B$ is

The depth at which the value of acceleration due to gravity becomes $\left(\frac{1}{n}\right)$ times the value at the surface of the earth is
( $\mathrm{R}=$ radius of the earth)

A uniform solid sphere of mass ' $m$ ' and radius ' r ' is surrounded by a uniform thin spherical shell of radius ' $2 r$ ' and mass ' $m$ ' then the gravitational field

The gravitational pull of the moon is $\left(\frac{1}{6}\right)^{th}$ of the earth and mass of moon is $\left(\frac{1}{8}\right)^{\text {th }}$ of the earth. This implies that the

Two satellites P and Q go round a planet in circular orbits having radii ' $3 R$ ' and ' $R$ ' respectively. If the speed of satellite $P$ is ' $2 V$ ', the speed of the satellite $Q$ will be

Time period of a simple pendulum on earth's surface is ' T '. It time period becomes ' xT ' when taken to a height ' $2 R$ ' above earth's surface. The value of $x$ will be $(R=$ radius of earth)

The magnitude of gravitational potential energy of a body at a distance ' $R$ ' from the centre of the earth is ' E '. Its weight at a distance ' 1.5 R ' from the centre of the earth is

Water rises up to height ' $x$ ' in a capillary tube immersed vertically in water. When the whole arrangement is taken to a depth ' $d$ ' in a mine, the water level rises up to height Y . If R is the radius of the earth then the ratio $\mat...

The total energy of a circularly orbiting satellite is

The radii of circular orbits of two satellites $A$ and $B$ of the earth are ' $4 R$ ' and ' $R$ ' respectively, where $R$ is the radius of earth. If the speed of satellite $B$ is 6 V , then the speed of satellite $A$ will be

A body is projected vertically from earth's surface with $\left(\frac{1}{3}\right)^{\mathrm{rd}}$ of escape velocity. The maximum height reached by the body is ( $R=$ radius of earth)

The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value then its new time period will become

Two particles of equal mass ' $m$ ' move in a circle of radius ' $r$ ' under the action of their mutual gravitational attraction. The speed of each particle will be ( $\mathrm{G}=$ Universal gravitational constant)

The escape velocity of a satellite from the surface of earth does NOT depend on

Two satellites A and B having ratio of masses $3: 1$ are revolving in circular orbits of radii ' $r$ ' and ' 4 r '. The ratio of total energy of satellites A to that of B is

The period of a planet around the sun is 8 times that of earth. The ratio of radius of planet's orbit to the radius of the earth's orbit is

The radius of the planet is double that of the earth, but their average densities are same. $\mathrm{V}_{\mathrm{p}}$ and $V_E$ are the escape velocities of planet and earth respectively. If $\frac{V_P}{V_E}=x$, the value of ' $x$ ' is

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 gravita...

If ' $R$ ' is the radius of earth & ' $g$ ' is acceleration due to gravity on earth's surface, then mean density of earth is

The height ' $h$ ' above the earth's surface at which the value of acceleration due to gravity $(\mathrm{g})$ becomes $\left(\frac{\mathrm{g}}{3}\right)$ is ( $\mathrm{R}=$ radius of the earth)

The escape velocity from earth surface is $11 \mathrm{~km} / \mathrm{s}$. The escape velocity from a planet having twice the radius and same mean density as earth is

A pendulum is oscillating with frequency ' $n$ ' on the surface of earth. If it is taken to a depth $\frac{R}{4}$ below the surface of earth, new frequency of oscillation of depth $\frac{\mathrm{R}}{4}$ is ( $\mathrm{R}=$ radius of earth)

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 c...

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

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

The height at which the weight of the body becomes $\frac{1^{\text {th }}}{16}$ of its weight on the surface of the earth of radius ' $R$ ' is

The height above the earth's surface at which the acceleration due to gravity becomes $\left(\frac{1}{n}\right)$ times the value at the surface is ( $R=$ radius of earth)

The magnitude of gravitational field at distance ' $r_1$ ' and ' $r_2$ ' from the centre of a uniform sphere of radius ' $R$ ' and mass ' $M$ ' are ' $F_1$ ' and ' $F_2$ ' respectively. The ratio ' $\left(F_1 / F_2\right)$ ' will be (if $r_...

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 ' $E_2$ '...