The mass of planet Jupiter is `1.9xx10^(27)kg` and that of the Sun is `1.99xx10^(30)kg`. The mean distance of Jupiter from the Sun is `7.8xx10^(11)`m. Calculate the gravitational force which Sun exerts on Jupiter. Assuming that Jupiter moves in circular orbit around the Sun, also calculate the speed of Jupiter `G=6.67xx10^(-11)Nm^(2)kg^(-2)`.

Options

A. `5 xx 10^(4) ms^(-1)`
B. `2 xx 10^(8) ms^(-1)`
C. `1.3 xx 10^(4) ms^(-1)`
D. `11 xx 10^(10) ms^(-1)`

Answer

C

Explanation

Here, `M_(J) = 1.9 xx 10^(27) kg`,
`M_(S) = 1.99 xx 10^(30) kg, r = 7.8 xx 10^(11) m`,
`g = 6.67 xx 10^(-11) Nm^(2) kg^(-2), F= ?`
Now `F = (GM_(J) M_(S))/(r^(2))`
`= (6.67 xx 10^(-11) xx 1.9 xx 10^(27) xx 1.99 xx 10^(30))/((7.8 xx 10^(11))^(2))`
`= 4.15 xx 10^(23)N`
Since, the gravitational pull of sun to jupiter provides the required centreipetal force to the jupiter, therefore, the velocity of the jupter `upsilon` can be given
`F = (M_(J) upsilon^(2))/(r )`
or `upsilon = sqrt((F r)/(M_(J))) = sqrt((4.15 xx10^(23) xx 7.8 xx 10^(11))/(1.9 xx 10^(27)))`
`= 1.3 xx 10^(4) ms^(-1)`