Gravitational Potential Energy

Q. The gravitational field in a region is given by g(vector)=(5N/kg i^) + (12N/kg j^). The change in the gravitational potential energy of a particle on mass 2 kg when it is taken from the origin to a point (7m, -3m) is

Q. 62. If g is the acceleration due to gravity on the earths surface, the gain in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius R of the earth, is A)1/4mgr B)1/2mgr C)2mgr D)mgr

Q. The magnitude of gravitational potential enegy of a body at a dis†an ce r from centre of earth is u.its weight nat a distamce 2r from centre of earth i

Q.

A small body starts falling on to the earth from a distance equal to the radius of the earths orbit. How long will the body take to reach the sun? Express the time in terms of T, period of revolution of the earth round the sun

1. 

2. 

3. 

4. T

Q. A spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system ? Mass of the space ship = 1000 kg; mass of the sun = 2×10³⁰ kg; mass of mars = 6.4×10²³ kg; radius of mars = 3395 km; radius of the orbit of mars = 2.28 ×10⁸ km; G = 6.67×10¯¹¹N m² kg₂.

Q. 87. Two point masses m are kept r distance apart . What will be the potential at 0.25r distance from any one mass towards the other mass?

Q. Four masses of $1\text{kg}$ each are placed to form a square as shown. What will be the magnitude of work required to double the length of the square keeping the masses at the corners?

1. $W=G\left(\frac{2\sqrt{2}+1}{\sqrt{2}}\right)$
   
2. $W=G\left(\frac{2\sqrt{2}-1}{3\sqrt{2}}\right)$
3. $W=G\left(\frac{2\sqrt{2}+1}{\sqrt{2}}\right)$
4. $W=G\left(\frac{2\sqrt{2}-1}{\sqrt{2}}\right)$

Q. 62. A mass M is broken intom two parts of masses m1 an m2 . How are m1 and m2 related so that foce of gravitational attraction between the two parts is maximum.?

Q. 47 A particle of mass M is situated at the centre of a spherical shell of same mass and radius a. The gravitational potential at a point situated at a/2 distance from centre will be

Q. Two bodies of mass 10 kg and 1000 kg are separated by a distance of 1 m. At what distance a mass of 1 kg should be placed between two masses so that it experiences no net gravitational attraction?

Q. At what height from the surface of earth the gravitational potential and value of g are -5.4×10^{7 } J/Kg^2 and 6m/s^2 respectively take R=6400Km

Q. 23.what is the acceleration due to gravity at a distance 3r from the center of earth if gratational potential at distance r from the centre of earth is v ? ( Assume r>R , where R = radius of Earth) 1) v/9r 2)v/3r 3)v/4r 4)v/2r

Q. the distance between two spherical bodies increased to two times then by how many times the mass of one of the body is to be changed to maintain the same gravitational force

Q. Two spherical bodies of mass m and 5m and radii R and 2R are released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller bodybegore collision is

Q. Gravitational law in vector form ? Gravitational potential energy ?

Q.

Mass M is divided into two parts x M and (1 - x)M. For a given separation, the value of x for which the gravitational attraction between the two pieces becomes maximum is

1. 1/2

2. 3/5

3. 1

4. 2

Q. Two spherical bodies of mass M and 5M ad radii R and 2R are released in free space with initial seperation between their centers =12R.If they attract each other due to gravitational force of attraction, dis†an ce covered by smaller body before collision is?

Q. If gravitational potential energy of earth and a block of mass m is taken zero at the surface then potential energy of this system at a height Re above the surface is- 1.mgR/2 2.mgR 3.-mgR /2 4.-mgR

Q. A stone is being projected at a speed of 10ms^{-1} from a 10m high building.The maximum possible range of the stone is