Question

The mass of the Jupiter is $1.9\times {10}^{27}$ kg and that of the sun is $1.99\times {10}^{38}$ kg. The mean distance of the Jupiter from the sun is $7.8\times {10}^{11}$ m. Speed of the Jupiter is (assuming that Jupiter moves in the circular orbit around the sun).

• A. $1.304\times {10}^4$ m/sec
• B. $13.04\times {10}^4$ m/sec
• C. $1.304\times {10}^8$ m/sec
• D. $1.304\times {10}^2$ m/sec

Answer 1

The correct option is C $1.304\times {10}^8$ m/sec

Jupiter mass $M_j=1.9\times {10}^{27}$

Sun mass $M_s=1.99\times {10}^{38}$

distance $r=7.8\times {10}^{11}$ all in $SI$ system of units

the centripetal force $\left(M_j{v}^2/r\right)$ for revolution will be provided by the gravitational attraction $G{M}_j{M}_s/r^2$

so equating both we get $M_j{v}^2/r=G{M}_j{M}_s/r^2$ which give us $v=\sqrt[2]{2\frac{G{M}_s}{r}}$

after putting $G=6.67\times {10}^{-11}N{m}^2/(Kg{)}^2$ and other values

we get $v=1.3\times {10}^{8}m/s$

Option C is correct.