Question

Calculate the workdone in moving a body of mass 1000 kg from a height 2 R to a height 3 R above the surface of the earth.

Answer 1

Answer:

mg(h2-h1)

1000×10(3r-2r)

10000r

10000×6400

Answer 2

Given :

Mass of body , m = 1000 kg .

To find :

The work done in moving a body from a height 2 R to a height 3 R .

( Here, R is radius of earth )

Solution :

We know , work done is given by :

$W=\int\limits^{3R}_{2R} {F} \, dr$        ...... ( 1 )

Here , F is the gravitational force and equal to , $F=\dfrac{GMm}{r^2}$

Therefore , work done is :

$W=\int\limits^{3R}_{2R} {\dfrac{GMm}{r^2}} \, dr\\\\W= GMm|-\dfrac{1}{r}|_{2R}^{3R}\\\\W= GMm(-\dfrac{1}{3R}+\dfrac{1}{2R})\\\\W=\dfrac{GMm}{6R}$

Putting all value in above equation .

We get :

$W=\dfrac{6.67\times 10^{-11}\times 6\times 10^{24}\times 1000}{6\times 6.4\times 10^6}\\\\W=1.04\times 10^{10}\ J$

Hence , this is the required solution .

Learn More :

Gravitational

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