Question

how much faster does a body fall on Jupiter considering that Jupiter is 300 times heavier than earth and 10 times bigger than Earth​

Answer 1

Answer:

3 times fastr I guess this is std12 gravitation

Answer 2

Explanation:

• The Newton's Law of Gravitation states for two objects, the attractive force between them is directly proportional to their individual masses product and also inversely proportional to the the square of the distance present between their centers.

             Mathematically   $F=G\frac{Mm}{R^{2} }$

Where,

$M$ is the greater mass that is attracting the smaller mass $m$ towards itself.

$R$ is the distance between their centers.

$G$ is the Universal gravitational constant $(G=6.67$ ×  $10^{-11}Nm^{2}/kg^{2})$

• We also know, The force of gravity acting on the mass $m$ which is equal to its weight on the earth's surface is given by                        

                                       $F=mg$  

If $M_{e}$ is the mass of earth that is attracting an object of mass $m$ then,

Equating both the value of forces, we get

$G\frac{M_{e} m}{R^{2} }=mg$

$g=\frac{GM_{e} }{R_{e} ^{2} }$              $(i)$

Therefore, the acceleration due to gravity is directly proportional to the mass of earth and inversely proportional to the square of the distance between its centers.

Solution:

According to the question,

Jupiter is 300 times the mass of earth $M_{J} =300M_{e}$  

Jupiter is 10 times bigger than earth $R_{J}=10R_{e}$

Hence, the value of g on Jupiter will be $g'$

$g'=\frac{GM_{J} }{R_{J} ^{2} }$             $(ii)$

and

$g'=G\frac{(300M_{e} )}{(10R_{e}) ^{2} }$

$g'=G\frac{300M_{e} }{100R_{e} ^{2} }$

$g'=3G\frac{M_{e} }{R_{e} ^{2} }$

We know,  $\frac{GM_{e} }{R_{e} ^{2} }=g$

$g'=3g$

Multiplying both side by time $t$, we get

$g't=3gt$

We know, the velocity of any object falling towards the surface of any planet is given by $v=gt$

Hence,

$V_{J}=3V_{e}$

The velocity of any object falling towards the surface of Jupiter will be 3 times more than the velocity of the object while coming towards the Earth's surface.