Gravitation Test - 9

Weight is a force caused by gravity. The weight of an object is the gravitational force between the object and the Earth. The more mass the object has the greater its weight will be. Weight is a force, so it's measured in newtons.

When any body or particle moves in circular orbit centripetal force acts on it and to move the object centripetal acceleration is necessary. So, when a satellite moves in circular orbit the centripetal acceleration is provided by the gravitational attraction of the earth.

It should be thrown with a velocity greater than or equal to escape velocity of the planet only then it will not return to Earth
Escape Velocity = √(2GM/R) = (2GM/R)^1/2 
Hence A is the correct answer.

As, U=−Gm₁m₂/r, 
it can be used to describe the potential energy in a system of point charges (or radially symmetric spheres) as a function of their separation distance r, then the maximum value is zero at infinite separation.
Hence, its maximum value is zero at infinity.
 

 Escape velocity does not depend on the angle of projection. Escape velocity will remain the same.
Hence, escape velocity is 11.2km/s .

In common usage, the initial point is on the surface of a planet or moon. On the surface of the Earth, the escape velocity is about 11.2 km/s, which is approximately 33 times the speed of sound (Mach 33) and several times the muzzle velocity of a rifle bullet (up to 1.7 km/s).

If velocity of satellite is is less than tge escape velocity then the satellite can go to certain hight and then cames back because the satellite is under the gravitational influence. therefore gravitational force acting on the satellite and due to this force satellite camse back

Escape velocity is the minimum velocity with which the body has to be projected vertically upwards from the surface of the earth so that it crosses the gravitational field of earth and never returns back on its own.

Gravitational Potential is dened as the potential energy of a particle of unit mass at that point due to the gravitational force exerted byearth. Gravitational potential energy of a unit mass is known as gravitational potential.

so, we see at the top most point the velocity the boy is zero and the earth's pull is acting downwards.
Given, g_m/g_e=1/6
=>g_e=6g_m
So using,
v² = u² - 2gs (where g=acceleration due to gravity, s=total height)
so,
0 = u² - 2gs
⇒ s=u²/2g_e
⇒ 2=u²/2g_e
Putting g_e =6g_m
⇒ 2=u²/g_m
⇒ 12=u²/2g_m
so the boy can jump a height of 12 m on the moon's surface.

Because geostationary satellite ( completes it's rotation in about 24hrs).and it's rotation cycle is same as that of Earth .thus it's velocity is zero with respect to earth

The gravitational potential at a point is defined as the work done in bringing the unit mass from infinity to that point without acceleration.

Gravitational potential is a scalar quantity. It is denoted by V. Its S.I. unit is J kg^-1. Its CGS unit is erg g-1

Dimensions of gravitational potential are [M⁰L²T^-2].

Gravitational Potential.Gravitational potential is the potential energy per kilogram at a point in a field. So the units are Jkg^-1, joules per kilogram.The equation for the potential: = -Gm/r.Potential is not a vector even though it has a -ve sign. It doesn't have direction only magnitude. So, it is scalar quantity.Hence, correct answer is (A).

We know that gravitational potential is negative in sign and its magnitude decreases when distance from the massive attracting object increases, hence when considered with sign we can say that gravitational potential increases with increases in distance.

Escape velocity is the minimum velocity with which the body has to be projected vertically upwards from the surface of the earth so that it crosses the gravitational field of earth and never returns back on its own.

Weight is a consequence of the universal law of gravitation: any two objects, because of their masses, attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. A mass is pulled towards the earth with “g” and thus comprises the weight of that body.

As the satellite is bounded by earth's gravitational field and has some velocity, it would completely revolve around the circular orbit without any external energy required.