Consider a planet whose mass and radius both are one half to that of Earth. An object of weight W on Earth will weigh ________ on that planet.

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Question

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RRB ALP Electrician 22 Jan 2019 Official Paper (Shift 2)

Answer 1

Concept:

Acceleration achieved by any object due to the gravitational force of attraction by any planet is called acceleration due to gravity by that planet.
\(g = G\frac {M}{r^2}\)
Where, G = universal gravitational constant = 6.67 × 10^-11Nm²/kg², M = mass of the planet, r = radius or distance from the center of that planet.
As each planet has a different mass and radius so the acceleration due to gravity will be different for different planets.
Weight is a measure of how heavy a person or object it.
W = mg
Where, m = mass of the object, g = acceleration due to gravity by that planet.

Calculation:

Let the mass of the earth is M and the radius is r,

Then the acceleration due to gravity is equal to, \(g = G\frac {M}{r^2}\)

And weight, W = mg = \(G\frac {Mm}{r^2}\)

Now, the mass of the planet M' = \(\frac M2\)and the radius, r' = \(\frac r2\)

Then the acceleration due to gravity is equal to \(g' = G\frac {2M'}{r^2} \)

And weight, W' = mg' = \(2 \times G\frac {Mm}{r^2}\) = 2W