Class 10 Science I Gravitation

The radius of planet A is half the radius of planet B. If the mass of A is MA, what must be the mass of B so that the value of g on B is half that of its value on A?

As per the question we can list the data as

$R_{A}=\frac{R_{B}}{2}$

$g_{B}=\frac{g_{A}}{2}$

To find -

$M_{B}=?$

Solution -

Using the formula of g

$g_{A}=\frac{GM_{A}}{R_{A}^{2}}$

$g_{B}=\frac{GM_{B}}{R_{B}^{2}}$

$\frac{g_{A}}{g_{B}}=\frac{\frac{GM_{A}}{R_{A}^{2}}}{\frac{GM_{B}}{R_{B}^{2}}$

$\frac{g_{A}}{g_{B}}=\frac{GM_{A}}{R_{A}^{2}}X\frac{R_{B}^{2}}{GM_{B}}$

$2=\frac{M_{A}}{R_{A}^{2}}X\frac{R_{B}^{2}}{M_{B}}$

$2=\frac{M_{A}}{R_{A}^{2}}X\frac{(2R_{A})^{2}}{M_{B}}$

$2=\frac{M_{A}}{R_{A}^{2}}X\frac{4R_{A}^{2}}{M_{B}}$

$2=\frac{4M_{A}}{M_{B}}$

$M_{B}=2M_{A}$

The mass of the earth is 6 x 10²⁴ kg. The distance between the earth and the Sun is 1.5x 10¹¹ m. If the gravitational force between the two is 3.5 x 10²² N, what is the mass of the Sun?