The acceleration due to gravity on the surface of earth is g. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be:
- g/4
- 4g
- g/2
- 2g
The Correct Option is B
Approach Solution - 1
To solve the problem, we need to understand how acceleration due to gravity, \(g\), depends on the dimensions and mass of the Earth. The formula for gravitational acceleration at the surface of a planet is given by:
\(g = \frac{G \cdot M}{R^2}\)
where:
- \(G\) is the gravitational constant.
- \(M\) is the mass of the Earth.
- \(R\) is the radius of the Earth.
According to the problem, the diameter of the Earth is reduced to half, which means the radius will also be reduced to half. So, the new radius \(R_{new} = \frac{R}{2}\).
Since the mass of the Earth remains constant, we can substitute \(R_{new}\) into the formula for gravity:
\(g_{new} = \frac{G \cdot M}{(R_{new})^2} = \frac{G \cdot M}{(\frac{R}{2})^2}\)
This simplifies to:
\(g_{new} = \frac{G \cdot M}{\frac{R^2}{4}} = \frac{4 \cdot G \cdot M}{R^2}\)
The above expression shows that the new acceleration due to gravity becomes:
\(g_{new} = 4g\)
Therefore, if the diameter of the Earth is reduced to half and the mass remains constant, the acceleration due to gravity on the surface of the Earth would be \(4g\), which corresponds to the correct answer: 4g.
Approach Solution -2
The acceleration due to gravity on the surface of the earth is given by:
\(g = \frac{GM}{R^2}\)
where \( G \) is the gravitational constant, \( M \) is the mass of the earth, and \( R \) is the radius of the earth.
If the diameter of the earth is reduced to half, the radius \( R \) will also be reduced to half, becoming \( \frac{R}{2} \). Substituting \( R' = \frac{R}{2} \) into the formula for \( g \), we get:
\(g' = \frac{GM}{(R/2)^2} = \frac{GM}{R^2/4} = 4 \cdot \frac{GM}{R^2} = 4g\)
Thus, the new acceleration due to gravity on the surface of the earth would be \( 4g \).
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Acceleration
In the real world, everything is always in motion. Objects move at a variable or a constant speed. When someone steps on the accelerator or applies brakes on a car, the speed of the car increases or decreases and the direction of the car changes. In physics, these changes in velocity or directional magnitude of a moving object are represented by acceleration.
