Question 392: Gravitation

Question

At what height from the surface of earth the gravitation potential and the value of g are $$-$$5.4 $$ 	imes $$ 10
7
J kg
$$-$$1
and 6.0 m s
$$-$$2
respectively?  Take the radius of earth as 6400 km.

Accepted Answer

As we know, gravitational potential (v) and acceleration due to gravity (g) with height
$$V = {{ - GM} \over {R + h}} =  - 5.4 	imes {10^7}$$   ...(i)
and $$g = {{GM} \over {{{\left( {R + h} ight)}^2}}} = 6$$   ...(ii)
Dividing (i) by (ii)
$${{{{ - GM} \over {R + h}}} \over {{{GM} \over {{{\left( {R + h} ight)}^2}}}}} = {{ - 5.4 	imes {{10}^7}} \over 6}$$
$$ \Rightarrow {{ - 5.4 	imes {{10}^7}} \over {\left( {R + h} ight)}} = 6$$
$$ \Rightarrow $$ R + h = 9000 km so, h = 2600 km

Answer

1400 km

Answer

2000 km

Answer

2600 km

Answer

1600 km

Gravitation

At what height from the surface of earth the gravitation potential and the value of g are $-5.4 \times 10 7 J kg -1 and 6.0 m s -$2 respectively? Take the radius of earth as 6400 km.

Choose the correct answer: