Gravitation Practice Level -1 - Class 11 MCQ

A space vehicle approaching a planet has a speed v,when it is very far from the planet. At that momenttangent of its trajectory would miss the centre of theplanet by distance R. If the planet has mass M andradius r, what is the smallest value of R in order thatthe resulting orbit of the space vehicle will just missthe surface of the planet?

The two planets with radii R₁,R₂ have densities ρ_1, ρ₂ and atmospheric pressures p₁ and p₂, respectively. Therefore, the ratio of masses of their atmospheres, neglecting variation of g and p within the limits of atmosphere, is

If g is the acceleration due to gravity on the earth’ssurface, the change in the potential energy of an objectof mass m raised from the surface of the earth to aheight equal to the radius R of the earth is

A space station is set up in space at a distance equalto the earth’s radius from the surface of the earth.Suppose a satellite can be launched from the spacestation. Let v₁ and v₂ be the escape velocities of thesatellite on the earth’s surface and space station,respectively. Then

The orbital velocity of an artificial satellite in a circularorbit just above the earth’s surface is v. For a satelliteorbiting at an altitude of half of the earth’s radius, theorbital velocity is

The distance of two planets from the Sun are 10¹³ and10¹² m, respectively. The ratio of time periods of thesetwo planets is

The gravitational force between two objects isproportional to 1/R (and not as 1/R²) where R isseparation between them, then a particle in circularorbit under such a force would have its orbital speed vproportional to

Two particles of equal mass go around a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is

A satellite of mass m is revolving around the earth atheight R radius of the earth) from the earth’s surface.Its potential energy will be

If g is same at a height h and at a depth d, then

A geostationary satellite orbits around the earth in acircular orbit of radius 36000 km. Then, the time periodof a spy satellite orbiting a few 100 km above the earth’ssurface (R_earth = 6400 km) will approximately be

if W₁,W₂and W₃ represent the work done in moving a particle —from A to B along three different paths 1,2 and 3, respectively, (as shown in the figure) in the gravitational field of a point mass m, find the correct relation between W₁ W₂ and W₃.

If R is the radius of the earth and g the accelerationdue to gravity on the earth’s surface, the mean densityof the earth is

A satellite moves around the earth in a circular orbitwith speed V lf m is the mass of the satellite, its totalenergy is

The value of g (acceleration due to gravity) at earth’ssurface is 10 ms^-2 Its value in m s^-2 at the centre of theearth which is assumed to be a sphere of radius Rmetre and uniform mass density is

Two satellites A and B of masses m₁ and m₂ (m = 2 m₂)are moving in circular orbits of radii r₁ and r₂ (r₁ = 4 r₂).respectively, around the earth. If their periods areT_A and T_B then the ratio T_A / T_B is

If three uniform spheres, each having mass M andradius R, are kept in such a way that each touches theother two, the magni-tude of the gravitational force onany sphere due to the other two is

If the radius of the earth decreases by 10%, the massremaining unchanged, what will happen to theacceleration due to gravity?

Two equal masses each m are hung from a balancewhose scale pans differ in vertical height by 'h'. Theerror in weighing in terms of density of the earth p is

The distances from the centre of the earth, where theweight of a body is zero and one-fourth that of the weightof the body on the surface of the earth are (assume Ris the radius of the earth)

Two bodies with masses M₁ and M₂ are initially at restand a distance R apart. Then they move directly towardsone another under the influence of their mutualgravitational attraction. What is the ratio of the distancestravelled by M₁ to the distance travelled by M₂?

If g is acceleration due to gravity on the earth’s surface,the gain the potential energy of an object of mass mraised from the surface of earth to a height equal to theradius R of the earth is