What will be the value of acceleration due to gravity on the surface of the earth if the radius of the earth suddenly decreases to 60% of its present value, keeping the mass of the earth unchanged?*1 point5.89 m/s^29.81 m/s^216.35 m/s^227.14 m/s^2
Question
What will be the value of acceleration due to gravity on the surface of the earth if the radius of the earth suddenly decreases to 60% of its present value, keeping the mass of the earth unchanged?*1 point5.89 m/s^29.81 m/s^216.35 m/s^227.14 m/s^2
Solution
The acceleration due to gravity (g) on the surface of the Earth is given by the formula:
g = 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 radius of the Earth decreases to 60% of its present value, the new acceleration due to gravity (g') would be:
g' = GM/(0.6r)^2
This simplifies to:
g' = GM/(0.36r^2)
Since GM/r^2 is the original acceleration due to gravity (g), we can substitute this into the equation to get:
g' = g/0.36
The current acceleration due to gravity on the surface of the Earth is approximately 9.81 m/s^2. Substituting this into the equation gives:
g' = 9.81 m/s^2 / 0.36 = 27.25 m/s^2
So, if the radius of the Earth were to decrease to 60% of its current value, the acceleration due to gravity on the surface of the Earth would increase to approximately 27.25 m/s^2. The closest answer to this is 27.14 m/s^2.
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