- Home
- Standard 11
- Physics
7.Gravitation
normal
The weight of a body on the surface of the earth is $63\, N$. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth ? (in $N$)
A
$35$
B
$28$
C
$18$
D
$40$
Solution
Acceleration due to gravity at altitude $h$ is given by
$g^{\prime}=\frac{g}{\left(1+\frac{h}{R_{e}}\right)^{2}}=\frac{g}{\left(1+\frac{R_{e} / 2}{R_{e}}\right)^{2}}$
$=\frac{g}{\left(1+\frac{1}{2}\right)^{2}}=\frac{g}{\left(\frac{3}{2}\right)^{2}}=\frac{4 g}{9} \ldots(i)$
Weight of the body at the earth's surface,
$w=m g=63 N-$……. $(ii)$
Weight of the body at altitude, $h=\frac{R_{e}}{2}$
$w^{\prime}=m g^{\prime}=\frac{4}{9} m g$ $…(iii)$
Using equation $(ii),$ we get
$w^{\prime}=\frac{4}{9} \times 63=28 N$
Standard 11
Physics
Similar Questions
normal
