The work done to raise a mass m from the surface of the earth to a height h. which is equal to the radius of the earth, is :

Question

The work done to raise a mass m from the surface of the earth to a height h. which is equal to the radius of the earth, is : (A) (1/2) mgR (B) (3/2) mgR (C) mgR (D) 2mgR

Tardigrade Admin · Accepted Answer

Initial potential energy at earths surface is

U_{i} = \frac{- GM m}{R}

Final potential energy at height h = R

U_{f} = \frac{- GM m}{2 R}

As work done = Change in PE

∴ W = U_{f} - U_{i}

= \frac{GM m}{2 R} = \frac{g R ^{2} m}{2 R} = \frac{m g R}{2} (∵ GM = g R^{2})

Q. The work done to raise a mass $m$ from the surface of the earth to a height $h$ . which is equal to the radius of the earth, is :

$\frac{1}{2} m g R$

$\frac{3}{2} m g R$

mgR

2mgR

Initial potential energy at earths surface is
$U_{i} = \frac{- GM m}{R}$
Final potential energy at height h = R
$U_{f} = \frac{- GM m}{2 R}$
As work done = Change in PE
$∴ W = U_{f} - U_{i}$
$= \frac{GM m}{2 R} = \frac{g R ^{2} m}{2 R} = \frac{m g R}{2} (∵ GM = g R^{2})$

Q. The work done to raise a mass m from the surface of the earth to a height h. which is equal to the radius of the earth, is :

21​mgR

23​mgR

mgR

2mgR

Initial potential energy at earths surface is Ui​=R−GMm​ Final potential energy at height h = R Uf​=2R−GMm​ As work done = Change in PE ∴W=Uf​−Ui​ =2RGMm​=2RgR2m​=2mgR​(∵GM=gR2)

Q. The work done to raise a mass $m$ from the surface of the earth to a height $h$ . which is equal to the radius of the earth, is :

$\frac{1}{2} m g R$

$\frac{3}{2} m g R$

Initial potential energy at earths surface is
$U_{i} = \frac{- GM m}{R}$
Final potential energy at height h = R
$U_{f} = \frac{- GM m}{2 R}$
As work done = Change in PE
$∴ W = U_{f} - U_{i}$
$= \frac{GM m}{2 R} = \frac{g R ^{2} m}{2 R} = \frac{m g R}{2} (∵ GM = g R^{2})$