Sage-Tips

What is the increase in the potential energy of the body with mass m taken to a height h which is equal to radius of Earth?

If a body of mass $m$ is moved to a height equal to the radius of the earth $R$ (above the surface, then the increase in its potential energy is $\dfrac{1}{2}mgR$. Hence, (C) is the correct option.

What is the gain in potential energy of an object of mass m?

Show that the gravitational potential energy of an object of mass m at height h on Earth is given by PEg = mgh.

What will be gain in potential energy of a body of mass m at a height equal to three times the radius of Earth?

$\therefore \vartriangle U = \dfrac{{mgh}}{{1 + \dfrac{h}{R}}}$ . Therefore, $\dfrac{{3mgR}}{4}$ will be gained in potential energy of a body of mass $’m’$ at a height equal to three times the radius $’R’$ of the earth. Hence, the correct option is (D) $\dfrac{{3mgR}}{4}$ .

What is the potential energy of a body on the earth surface?

gravitational potential energy
Near the surface of the Earth, the work done in lifting an object through a height h is the product mgh , so U=mgh . The gravitational potential energy, U , of a system of masses m1 and M2 at a distance r using gravitational constant G is U=−Gm1M2r U = − G m 1 M 2 r .

What is the energy required to move a body of mass m?

Energy required to move a body of mass m from an orbit of radius 2R to 3R. The two orbits will have different gravitational potential energies. Energy required to move from one orbit to another is equal to change in gravitational potential energy.

What is the gain in potential energy?

When work is done on object energy is transferred to the object and it gains gravitational potential energy. If the same object falls from that height, the same amount of work would have to be done by the force of gravity to bring it back to the Earth’s surface.

What will increase the gravitational potential energy of an object of mass m raised through a height h from the earth surface?

An object’s gravitational potential is due to its position relative to the surroundings within the Earth-object system. The force applied to the object is an external force, from outside the system. When it does positive work it increases the gravitational potential energy of the system.

What will be gain in potential energy of a body?

When an object is lifted the work is done against the gravity. When work is done on object energy is transferred to the object and it gains gravitational potential energy.

What will be gain in potential energy?

Since the gravitational potential energy of an object is directly proportional to its height above the zero position, a doubling of the height will result in a doubling of the gravitational potential energy. A tripling of the height will result in a tripling of the gravitational potential energy.

What is the increase in gravitational potential energy of the system?

The increase in gravitational potential energy of the system is : The work done by an external agent to shift a point mass from infinity to the centre of the earth is W. Then choose the correct relation. A particle of mass m 1 ​ lies inside a spherical shell of mass m 2 ​ and radius R at a distance r from the centre.

Is it safe to assume potential energy as MGH?

Normally for short distances it is safe to assume potential energy as ‘mgh’. However it has to be noted that ‘g’ is the result of universal gravitational force which is GMm/r^2. Hence gravitational force is depended on the distance between the two masses. At surface of earth the gravitational force, mg=GMm/R^2 where ‘R’ is the radius of earth.

When does potential energy of an object reach its terminal velocity?

Potential energy applies before the object has reached escape velocity or otherwise enters orbit.Also, potential energy has a diminishing return with an object’s terminal velocity.

How much more mass does the Earth gain each year?

NASA says that Earth gains about 160 tonnes of matter a year because the global temperature is going up:”If we are adding energy to the system, the mass must go up.” Oh, those crazy thermodynamics. No effect• Of course, having more people or building stuff doesn’t add any mass to the planet.