Question

A planet of mass $3\times {10}^{29}$ gm moves around a star with a constant speed of $2\times {10}^{8}m{s}^{-1}$ in a circle of radii $1.5\times {10}^{12}$m. The gravitational force exerted on the planet by the star is

• A. $6.67\times {10}^{22}$ dyne
• B. $6.67\times {10}^{26}$ N
• C. $8\times {10}^{26}$ N
• D. $8\times {10}^{27}$ dyne

Answer 1

Answer: (C)

$8\times {10}^{26}$ N

Gravitational force supplies centripetal force
$\because F=\frac{m{v}^2}{r}=\frac{3\times {10}^{29}\times (2\times {10}^8{)}^2}{1.5\times {10}^{14}}$ dynes
$=8\times {10}^{31}$ dyne $=8\times {10}^{26}N(\because 1N={10}^5$ dyne. $)$