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Suppose a planet exists whose mass and radius both are half of that of the earth. Calculate the acceleration due to gravity on the surface of this planet.

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19.6

m/s2

9.8

m/s2

4.9

m/s2

0

m/s2

answer is A.

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Detailed Solution

The acceleration due to gravity on the surface of this planet is

19.6 m / s^{2}

.
Given data and assumptions:
Let the mass of the planet,

M_{p} = \frac{M_{e}}{2}

Mass of the earth,

= M_{e}

Let the radius of the planet,

R_{p} = \frac{R_{e}}{2}

Radius of the earth,

= R_{e}

Accelerationn due to gravity on earth,

g_{e} = 9.81 m / s^{2}

Acceleration due to gravity on the planet is

= g_{p}

We know, acceleration due to gravity on the earth is given by the formula,

\Rightarrow

g_{e} = \frac{G \times M_{e}}{{R_{e}}^{2}}

Now put the corresponding values of the planet in the above formula,

\Rightarrow

g_{p} = \frac{G \times M_{p}}{{{(R}_{p})}^{2}}

\Rightarrow

g_{p} = \frac{G \times \frac{M_{e}}{2}}{{(\frac{R_{e}}{2})}^{2}}

\Rightarrow

g_{p} = \frac{4 \times G \times M_{e}}{{2 \times R_{e}}^{2}}

\Rightarrow

g_{p} = \frac{2 \times G \times M_{e}}{{R_{e}}^{2}}

\Rightarrow

g_{p} = 2 \times

g_{e}

\Rightarrow

g_{p} = 2 \times 9.8 m / s^{2}

\Rightarrow

g_{p} = 19.6 m / s^{2}

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Suppose a planet exists whose mass and radius both are half of that of the earth. Calculate the acceleration due to gravity on the surface of this planet.

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