Sage-Tips

What is the gravitational potential inside a sphere?

Gravitational Potential of a Spherical Shell Now, Case 1: If point ‘P’ lies Inside the spherical shell (rV = -GM/R.

How is gravitational potential derived?

Gravitational potential energy is energy an object possesses because of its position in a gravitational field. Since the force required to lift it is equal to its weight, it follows that the gravitational potential energy is equal to its weight times the height to which it is lifted. PE = kg x 9.8 m/s2 x m = joules.

What is the derivation of potential energy?

Potential energy is defined as the energy that is held by an object because of its position with respect to other objects. The SI unit of potential energy is joule whose symbol is J. Potential energy term was introduced by Scottish engineer and physicist William Rankine in the 19th century.

What is the value of G in SI system?

In SI units, G has the value 6.67 × 10-11 Newtons kg-2 m2.

What is the difference between gravitational PE and PE?

Potential energy is energy that is stored in an object or substance. Gravitational potential energy is energy in an object that is held in a vertical position. Elastic potential energy is energy stored in objects that can be stretched or compressed.

What is gravitational potential energy write the SI unit of gravitational potential energy?

SI unit of gravitational potential is J/Kg. It is the potential body arising out of the force of gravity. If due to the force, if the position changes, then the change in the potential energy is the work done on the body by the force.

What is the gravitational potential in a uniform sphere?

Potential Due to a Uniform Sphere. According to Equation ( 897 ), the gravitational potential inside a uniform sphere is quadratic in . This implies that if a narrow shaft were drilled though the center of the sphere then a test mass, , moving in this shaft would experience a gravitational force acting toward the center which scales linearly in .

How do you find the potential energy of a self-gravitating sphere?

For a self-gravitating sphere of constant density , mass M, and radius R, the potential energy is given by integrating the gravitational potential energy over all points in the sphere, (Kittel et al. 1973, pp. 268-269).

How to derive the gravitational field intensity of a hollow sphere?

It is quite easy to derive the gravitational field intensity at a point within a hollow sphere. However, the result is quite surprising. The field intensity at any point within a hollow sphere is zero.

What is the derivation of the gravitational potential energy equation?

Derivation of Gravitational Potential Energy Equation. Consider a source mass ‘M’ is placed at a point along the x-axis, initially, a test mass ‘m’ is at infinity. A small amount of work done in bringing it without acceleration through a very small distance (dx) is given by. dw = Fdx. Here, F is an attractive force and the displacement is