The value of g at a certain height h above the free surface of the earth is x / 4 where x is the value of g at the surface of the earth. The height h is

Question

The value of g at a certain height h above the free surface of the earth is x / 4 where x is the value of g at the surface of the earth. The height h is (A) R (B) 2 R (C) 3 R (D) 4 R

Tardigrade Admin · Accepted Answer

x=(G M/R2) Again, (x/4)=(G M/(R+h)2) or x=G M((2/R+h))2 ∴ (1/R2)=((2/R+h))2=(2/R+h) or R+h=2 R or h=R

Q. The value of $g$ at a certain height $h$ above the free surface of the earth is $x /4$ where $x$ is the value of $g$ at the surface of the earth. The height $h$ is

R

2 R

3 R

4 R

$x = \frac{GM}{R ^{2}}$
Again, $\frac{x}{4} = \frac{GM}{( R + h ) ^{2}}$
or $x = GM (\frac{2}{R + h})^{2}$
$∴ \frac{1}{R ^{2}} = (\frac{2}{R + h})^{2} = \frac{2}{R + h}$
or $R + h = 2 R$ or $h = R$

Q. The value of g at a certain height h above the free surface of the earth is x/4 where x is the value of g at the surface of the earth. The height h is

R

2 R

3 R

4 R

x=R2GM​ Again, 4x​=(R+h)2GM​ or x=GM(R+h2​)2 ∴R21​=(R+h2​)2=R+h2​ or R+h=2R or h=R

Q. The value of $g$ at a certain height $h$ above the free surface of the earth is $x /4$ where $x$ is the value of $g$ at the surface of the earth. The height $h$ is

$x = \frac{GM}{R ^{2}}$
Again, $\frac{x}{4} = \frac{GM}{( R + h ) ^{2}}$
or $x = GM (\frac{2}{R + h})^{2}$
$∴ \frac{1}{R ^{2}} = (\frac{2}{R + h})^{2} = \frac{2}{R + h}$
or $R + h = 2 R$ or $h = R$