The height at which the weight of a body beco | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The acceleration due to gravity at a height $h$ from the surface of the Earth is given by:$g' = \frac{g}{(1 + \frac{h}{R})^2} \quad ... (i)$Where

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) The acceleration due to gravity at a height $h$ from the surface of the Earth is given by:$g' = \frac{g}{(1 + \frac{h}{R})^2} \quad ... (i)$Where $g$ is the acceleration due to gravity at the surface of the Earth and $R$ is the radius of the Earth.Multiplying both sides by the mass of the body $m$,we get the weight $W'$ at height $h$:$W' = mg' = \frac{mg}{(1 + \frac{h}{R})^2} = \frac{W}{(1 + \frac{h}{R})^2}$According to the question,$W' = \frac{1}{16}W$.Substituting this into the equation:$\frac{1}{16} = \frac{1}{(1 + \frac{h}{R})^2}$Taking the square root on both sides:$1 + \frac{h}{R} = 4$$\frac{h}{R} = 3$$h = 3R$

The height at which the weight of a body becomes $\frac{1}{16}^{th}$ of its weight on the surface of the Earth (radius $R$) is: (in $R$)

Similar Questions

The value of acceleration due to gravity at a height of $10 \,km$ from the surface of the Earth is $x$. At what depth inside the Earth is the value of the acceleration due to gravity the same value $x$ (in $\,km$)?

What should be the angular velocity of the Earth due to rotation about its own axis so that the weight of an object at the equator becomes $3/5$ of its initial value? (Radius of Earth at the equator is $R = 6400 \, km$,take $g = 10 \, m/s^2$)

The weight of a body at the surface of earth is $18 \, N$. The weight of the body at an altitude of $3200 \, km$ above the earth's surface is $........ \, N$ (given,radius of earth $R_e = 6400 \, km$).

The variation of acceleration due to gravity $g$ with distance $d$ from the centre of the earth is best represented by ($R =$ Earth's radius)

The force of gravity is least at:

Vedclass Test Series

Exam Paper Generator

Online Exam Module