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 a circular orbit around the sun)

• A. $1.304\times {10}^{4}m/sec$.
• B. $13.04\times {10}^{4}m/sec$.
• C. $1.304\times {10}^{6}m/sec$.
• D. $1.304\times {10}^{2}m/sec$.

Answer 1

The correct option is A $1.304\times {10}^{4}m/sec$.

$F=\frac{GMm}{r^2}$

$=\frac{6.67\times {10}^{-11}\times (1.99\times {10}^{30})\times (1.9\times {10}^{27})}{(7.8\times {10}^{11}{)}^2}$

$=4.14\times {10}^{23}N$

Now let its speed of jupiter be $v$, then

$F=\frac{m{v}^2}{R}$

$\Rightarrow v=\sqrt{\frac{FR}{m}}$

$=\sqrt{\frac{(7.8\times {10}^{11})\times (4.10\times {10}^{23})}{(1.9\times {10}^{27})}}$

$=1.304\times {10}^{4}m/sec$.