The escape velocity for a body projected vertically upwards from the surface of the earth is 11.2 km s-1. If the body is projected in a direction making an angle 45° with the vertical, the escape velocity will be
A projectile is fired vertically upwards from the surface of the earth with a velocity Kve , where ve is the escape velocity and k < 1. If R is the radius of the earth, the maximum height to which it will rise, measured from the centre of the earth, will be (neglect air resistance)
The radius of a planet is R. A satellite revolves aroundit in a circle of radius r with angular velocity ω0 . Theacceleration due to the gravity on planet’s surface is
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 ρ1, 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 (Rearth = 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 areTA and TB then the ratio TA / TB 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