Question

A man weighs 600 N at earth's surface at what height above the surface of Earth will he weigh 300 Newton take radius of the earth to be 6400 km .
please answer this question step by step.
(Answer is 1600 km)

Answer 1

Explanation:

First of all on Earth's surface g is 10m/s2

so the mass of the man is : 600/10 kg

= 60 kg .

so when it's taken to a height x above the Earth's surface its weight is 300 N.

then g there will be : (300/60)m/s2

= 5 m/s2

Now we know on going away from the Earth's surface the acceleration due to gravity decreases eventually .

it can be expressed by the formula

g' = g/(1+h/R)^2

here,

g' = g/2

R = 6400km

so putting the values

g/2 = g/(1+h/6400)^2

or , 1/2 = (1+h/6400)^-2

or , 1/2 = (1-2h/6400) [ applying the law of binomial theorem ]

or, h = 1600 km.