A solid sphere of uniform density and radius R applies a gravitational force of attraction equal to on a particle placed at P, distance 2R from the centre O of the sphere. A spherical cavity of radius R/2 is now made in the sphere as shown in fig. The sphere with the cavity now applies a gravitational force on the same particle placed at P. The ration will be :
1. 1.2
2. 7/9
3. 3
4. 7
If both the masses and radius of the earth, each decrease by 50%, the acceleration due to gravity would :
1. remain the same
2. decreases by 50%
3. decreases by 100%
4. increases by 100%
Two spherical planets A and B have same mass but, densities in the ratio 8:1. For these planets, the ratio of acceleration due to gravity at the surface of A to its value at the surface of B is :
1. 1:4
2. 1:2
3. 4:1
4. 8:1
Two equal masses m and m are hung from a balance whose scale pans differ in height by h. If is the mean density of the earth, then the error in weighing is :
1. zero
2.
3.
4.
At what height in km, above the earth's pole, the free-fall acceleration decreases by one percent? (Assume the radius of the earth to be 6400 km)
1. 32 km
2. 64 km
3. 80 km
4. 1.253 km
The distance from the centre of the earth where the weights of the body are zero and one fourth that of the weight of body on the surface of earth are : (taking radius of earth as R)
1. 0,
2. 0,
3. ,0
4. ,0
What would be the speed with which the earth has to rotate on its axis so that a person on the equator would weigh (3/5)th as much as present? Given the equatorial radius is R.
1.
2.
3.
4. 2g/5R
The gravitational field due to mass distribution is in the x-direction. Here C is constant. Taking the gravitational potential to be zero at infinity, the potential at x is :
1.
2.
3.
4.
A particle of mass m is placed at the centre of a uniform spherical shell of mass 3m and radius R. The gravitational potential on the surface of the shell is :
1.
2.
3.
4.
If g is the acceleration due to gravity on the earth's surface, the gain in potential energy of the body at a height equal to two times the radius R of the earth will be :
1. mg 2R
2. mg 3R
3.
4.
If body is released from a point at a height equals to n times the radius of the earth R, its velocity on reaching the surface of the earth is :
1.
2.
3.
3.
An artificial satellite revolves around the earth in a circular orbit with a speed v. If m is the mass of the satellite, its total energy is :
1.
2.
3.
4.
A satellite is orbiting around the earth. The centripetal force on the satellite is F. The gravitational force of the earth on the satellite is also F. The net force on the satellite is :
1. F
2. zero
3. 2F
4. F/2
If is the time period of the surface satellite of the earth, the height of parking orbit above the surface of the earth is about 6 times radius of the earth, the time period of parking satellites in terms of is :
1.
2.
3.
4.
Two particles of equal mass go round a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is :
1.
2.
3.
4.