Question

at which height from the earth urface at which acceleration due to gravity decreased by 75% of its value at earth surface?

Answer 1

i tried it by using formula
g=g/(1-h/R)^2
not getting my ans

Answer 2

Well, in general
F = ma
and the force due to gravity acting on a mass m is
F = - GMm/R^2
where G is the universal constant of gravity, M the mass of the earth and R the radius of the earth.

Combining the two equations: for a mass m--like you or me or my cat--at the earth surface, it experiences an acceleration of

a = - GM/R^2

Now ...

Answer 3

The one thing we're varying is the radial distance from the center of the earth. Let's write our radial distance as r = R + h, where h is the height. Then the question is:

For what value of h is

\[ \frac{GM}{r^2} = \frac{3}{4} \frac{GM}{R^2} \]

Answer 4

but it have no connection with this que we have to ue direct formula as in compettition only1 min is enough for one ques i think so..

Answer 5

Well, this is how you solve it. Given that, what is an expression for h?

Answer 6

for thi we had a formula but i m unable to solve this a it is becoming more complex
gh=g/(1+h/r)^2

Answer 7

I don't know where that formula comes from. Are you following my logic however?

Answer 8

acc. to ur solution we cant find the heigh as we have totake out an in a comparision way am i rit sir?? actually i m v.bad in physics frankly sayin

Answer 9

We can find it. r = R + h. Hence, from using the last equation I wrote down,

\[ r^2 = \frac{4}{3}R^2 \]
\[ (R+h)^2 = \frac{4}{3}R^2 \]
\[ R + h = \sqrt{4/3} R \]

Now solve that for h.

I strongly recommend you read what I wrote above and ask me questions about it. What I have written down is exactly the logic for getting to the answer.

Answer 10

i tried sir but not getting ans by dis too :(
the ans is h=Re
Re is radius of earth surface

Answer 11

Do you agree F = ma?

Answer 12

yes and what ur saying i already did that we had a derivetion by which concluded the formula to find h at altitude that is gh=g/(1+h/r)^2
do u want to see the derivation??

Answer 13

Where is 3/4 or 75% in your formula?

Answer 14

plz solve this que by your method firt if i had objection i ll ask u ok

Answer 15

its a general formula sir by which we can use it every where

Answer 16

I have solved it for you. There's one small step of algebra left.

Read my solution and ask me questions about it if you like.

Answer 17

but the ans is Re
and what the way u said ans is not coming :(

Answer 18

Oh, misread the question. The acceleration is decreased BY 75%, not to 75%. My mistake.

If it is decreased by 75%, then it 1/4 of what it was, hence

\[ \frac{GM}{r^2} = \frac{1}{4} \frac{GM}{R^2} \]
which implies
\[ r^2 = 4 R^2 \]
i.e.,
\[ (R+h)^2 = 4 R^2 \]
\[ R + h = 2R \]
\[ h = R \]

Answer 19

thanQ..

Answer 20

had one more ques hold on i m posting it

Answer 21

post it on the left