An object of mass m is raised from the surface of the earth to a height equal to the radius of the earth, that is, taken from a distance R to 2R from the centre of the earth. What is the gain in its potential energy?

This is a  Short Answer Type Questions as classified in NCERT Exemplar

Explanation-potential energy of the objects at the surface of the earth is =- $\frac{GMm}{R}$

PE of the object at a height equal to radius of earth = $\frac{GMm}{2R}$

Gain in potential energy = $\frac{GMm}{2R}$ - (- $\frac{GMm}{R}$ )= $\frac{GMm}{2R}$

= $\frac{g{R}^{2}m}{2R}=\frac{1}{2}mgR$ (GM=gR²)

<p>This is a &nbsp;Short Answer Type Questions as classified in NCERT Exemplar</p><p><strong>Explanation-</strong>potential energy of the objects at the surface of the earth is =-<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mi>G</mi> <mi>M</mi> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mi>R</mi> </mrow> </mrow> </mfrac> </math> </span></p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1745474425phpwHMC4t_480x360.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1745474425phpwHMC4t.jpeg" alt="" width="248" height="152"></picture></div></div><p>PE of the object at a height equal to radius of earth =<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mi>G</mi> <mi>M</mi> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> <mi>R</mi> </mrow> </mrow> </mfrac> </math> </span></p><p>Gain in potential energy =<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mi>G</mi> <mi>M</mi> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> <mi>R</mi> </mrow> </mrow> </mfrac> </math> </span> - (-<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mi>G</mi> <mi>M</mi> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mi>R</mi> </mrow> </mrow> </mfrac> </math> </span>)=<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mi>G</mi> <mi>M</mi> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> <mi>R</mi> </mrow> </mrow> </mfrac> </math> </span></p><p>= <span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mi>g</mi> <msup> <mrow> <mrow> <mi>R</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> <mi>R</mi> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> <mi>m</mi> <mi>g</mi> <mi>R</mi> </math> </span> (GM=gR²)</p>

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