If g is the acceleration due to gravity of the earth’s 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

  • Option 1)

    \frac{1}{2} mgR

  • Option 2)

    2 mgR

  • Option 3)

    mgR

  • Option 4)

    \frac{1}{4} mgR

 

Answers (1)

As we learnt in 

Gravitational Potential energy at a point -

W=-\frac{GMm}{r}

U=-\frac{GMm}{r}

U\rightarrow gravitational potential energy 

M\rightarrow Mass of source body

m\rightarrow mass of test body

r\rightarrow distance between two

- wherein

Always negative in the gravitational field because Force is attractive in nature.

 

 Potential energy at earth's surface =-\frac{GMm}{R}=-mgr

Potential energy at height R=-\frac{mgR}{2}

\therefore gain in potential energy =-\frac{mgR}{2}+mgR=\frac{mgR}{2}

 


Option 1)

\frac{1}{2} mgR

This is correct option

Option 2)

2 mgR

This is incorrect option

Option 3)

mgR

This is incorrect option

Option 4)

\frac{1}{4} mgR

This is incorrect option

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