Question

A body of mass m rises to height h = R/5 from
the earth's surface, where R is earth's radius. If g
is acceleration due to gravity at earth's surface,
the increase in potential energy is-​

Answer 1

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Answer 2

Answer:

The increase in potential energy is- $P E_1=\frac{5}{6} m g h$

Explanation:Step 1: Potential energy in physics is the energy that an object retains as a result of its location in relation to other objects, internal stresses, electric charge, or other elements.Energy that is conserved or kept in a substance or object is known as potential energy. The position, arrangement, or condition of the item or substance determines the amount of stored energy. It can be pictured as energy with the "potential" to perform labour.Any item that is raised from rest has energy that can be released at a later time; for this reason, it is referred to as potential energy.

Step 2: Potential energy is the energy that is stored in any object or system as a result of its location or component arrangement. The environment outside of the object or structure, such as air or height, has no impact on it. In contrast, kinetic energy refers to the energy of moving particles within a system or an item.

$Given \ h=\frac{R}{5} Potential \ Energy \ at \ surface \ of \ the \ earth,\left(P E_1\right)=-\frac{G M m}{R}$

${ Potential Energy at height } h=\frac{R}{5},\left(P E_2\right)$

$-\frac{G M m}{R+\frac{R}{5}}=-\frac{5 G M m}{6 R}$

$\text { Increase in Potential energy }=P E_2-P E_1=$$-\frac{5 G M m}{6 R}+\frac{G M m}{R}=\frac{G M m}{6 R}$

$\text { (Using } \left.g=\frac{G M}{R^2} \text { and } h=\frac{R}{5}\right) \Rightarrow P E_2-$

$P E_1=\frac{5}{6} m g h$

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