Question

**
If a planet existed whose mass and radius were both half those of the earth, what would be the
value of acceleration due to gravity on its surface as compared to what it is on the earth's
surface?
​

Answer 1

Answer:

$19.6m/s^2.$

Explanation:

Let $F$ be the force by which a planet of mass $M$ and radius $R$ attracts a body of mass $m$.

Let the mass of earth be $M$.

Let the mass of the other panet be $M'$.

We know that $M' = \dfrac{M}{2}$.

Let the radius of the earth be $R$

Let the radius of the other planet be $R'$.

We know that $R' = \dfrac{R}{2}$.

Let the mass of an imaginary body be $m$.

From the law of gravitation, we know that:

$F = \dfrac{GMm}{R^2}$ where $G$ is the universal gravitational constant.

$F' = \dfrac{GM'm}{(R')^2}$

$F' = \dfrac{G\dfrac{M}{2}m}{\Bigg(\dfrac{R}{2}\Bigg)^2}$

$F' = \dfrac{GMm}{2} \times \dfrac{4}{R^2}$

$F' = \dfrac{2GMm}{R^2}$

Substitute the value of $F$.

$F' = 2F$.

By the second law of motion, we know that $F = ma$.

Here $a = g$.

$mg' = 2mg$

$g' = 2g$

$g' = 2 \times 9.8m/s^2$

$\therefore g' = 19.6m/s^2$

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