Question

A body is suspended from a spring balance placed on a ground in the earth. The reading of the balance is $100g$. When the body is placed in a satellite which is revolving in a an orbit of radius $2R$, the reading is $W_1$. What is $W_1$? ($R$ is the radius of earth)

• A. $100g$
• B. $200g$
• C. $400g$
• D. $0$

Answer 1

The correct option is D $0$

Given, the weight of the body on the earth surface, $W=100g$


The orbital velocity of a satellite revolving around a planet of mass $M$ in an orbit of radius $r$ is given by $$v=\sqrt{\frac{GM}{r}}$$Since, the velocity of the body inside the satellite will be same as the orbital velocity of the planet, so the centrifugal force acting on the body will be,
$F_c=\frac{m{v}^2}{r}$

$\Rightarrow F_c=\frac{m{\left(\sqrt{\frac{GM}{r}}\right)}^2}{r}$

$\Rightarrow F_c=\frac{GMm}{r^2}...\left(1\right)$

Gravitational force acting on the body will be,

$F_g=\frac{GMm}{r^2}...\left(2\right)$

So, from free body diagram for a body hanging in the satellite,

$T+F_c=F_g$ ​

where, $T$ is the tension produced in spring balance.

Substituting the values from equation $\left(1\right)$ and $\left(2\right)$,

$\Rightarrow T+\frac{GMm}{r^2}=\frac{GMm}{r^2}$

$\Rightarrow T=0$

If weight $W_1$ is measured by the spring balance at $r=2R$, then

As, for spring balance $T=W_2=0$

Thus, so the becomes weightlessness inside a satellite revolving in any arobit.

So, option (d) is correct answer.

$\text{Alternate Solution:}$
For a satellite revolving around the earth at any orbital radius, the gravitational force towards earth is countered by centrifugal force $F_g=F_c$

So, for a body hanging in the satellite,

$W_2+F_c=F_g$

$\Rightarrow W_2=0$

Hence, option (d) is the correct answer.

Why this question: Any satellite in its circular orbit will not apply any reaction force and hence weightlessness will be felt inside a satellite.