A body suspended from a spring balance is placed in a satellite. Reading in balance is W₁ when the satellite moves in an orbit of radius R. Reading in balance is W₂ when the satellite moves in an orbit of radius 2R . Then

The correct option is W₁ = W₂.

Let's understand the physical principles behind this result step-by-step:

1. Concept of Weightlessness in a Satellite:
When a satellite orbits the Earth, it is in a state of continuous free fall towards the Earth. The gravitational force acting on any object of mass $m$ inside the satellite provides the centripetal acceleration required to keep it in its circular orbit.

The gravitational acceleration at an orbital radius $r$ is given by:
$a=\frac{GM}{r^2}$
where $G$ is the universal gravitational constant and $M$ is the mass of the Earth.

2. Analyzing the forces on the suspended body:
For a body of mass $m$ suspended from a spring balance inside the satellite, the forces acting on it are:
- The gravitational force pulling it towards the center of the Earth:
$F_g=\frac{GMm}{r^2}$
- The tension or restoring force exerted by the spring balance, which represents the weight reading $W$ of the balance.

Since the body moves in the orbit with the same acceleration $a$ as the satellite, we write the equation of motion as:
$F_g-W=ma$

Substituting the values of gravitational force $F_g$ and acceleration $a$:
$\frac{GMm}{r^2}-W=m\left(\frac{GM}{r^2}\right)$

Simplifying the equation, we get:
$W=0$

3. Comparing the readings at different radii:
Since the reading $W$ of the spring balance is zero, it remains zero regardless of the radius of the orbit.
- At orbital radius $R$, the reading is $W_1=0$.
- At orbital radius $2R$, the reading is $W_2=0$.

Therefore:
$W_1=W_2$