Question

Two persons A and B have spring balances and blocks of mass 4kg hanging from them. Person A measures the reading of spring balance on a planet whose mass is half of the earth and radius is twice of the earth. Person B takes the reading on the surface of a planet whose mass is twice of the earth and radius is three times of the earth. The ratio of reading of spring balance taken by A and B is

Options:
1. 9/16
2.9/8
3.8/9
4.9/2​

Answer 1

Answer:

9/16

Explanation:

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Answer 2

Given:

Mass of the block = 4 kg

A measures the reading on a planet that has half of the mass and twice the radius of the earth

B measures the reading on a planet that has twice mass and three times radius of the Earth.

To find:

The ratio of reading of the spring balance taken by A and B.

Solution:

The spring balance calculates the gravitational force acting on an object:

F = GMm/ r²

Where G = universal gravitational constant

M = mass of Earth

m = mass of object

r = radius of Earth

For A:

F = G(M/2)m / (2r)²

F = GMm / 8r²

For B:

F = G(2M)m/(3r)²

F = 2GMm / 9r²

Ratio of A and B = GMm/8r² / 2GMm/9r²

= 9/16

Therefore the required ratio is 9/16.