Question

Explorer- $38$, a radio-activity research satellite of mass $200kg$ circles the earth in an orbit of radius $3R/2$, where $R$ is the radius of the earth. Assuming the gravitational pull on a mass of $1kg$ at the earth's surface to be $10N$, the pull on the satellite is :

• A. $889N$
• B. $4500N$
• C. $9000N$
• D. None

Answer 1

The correct option is A $889N$

Force on the mass 1 kg on surface of earth:$F=\frac{G{M}_{e}m}{R^2}=\frac{G{M}_e\times 1}{R^2}=10N$

where $M_e$ is the mass of earth and R is the radius of earth.
Force on the satellite having mass $m_s$ at $\frac{3R}{2}$

is $\frac{G{M}_e{m}_s}{(\frac{3R}{2}{)}^2}=\frac{G{M}_e}{R^2}\times \frac{4m_s}{9}=10\times \frac{4\times 200}{9}=\frac{8000}{9}=889N$