Question

Hence, the force of gravitation between Earth and Jupiter is 8.16 * 10 N

Enample 5: An apple with the mass of 200 g falls from a tree. What is the acceleration
of the apple towards the earth? What is the acceleration of the earth towards the apple?
(Given: mass of the earth = 6*10kg radius of the earth 6.4 10 m, G=6.67 * 10 " Nm
kg and neglecting height of the tree).​

Answer 1

Acceleration of the apple towards the earth is: 9.7705 m/s2.

Acceleration produced on earth towards the apple

`0.325*10^(-24) \ \ m/s2.`

Step-by-step explanation:

Given :

`m = 200 g`

We have to convert into the kg ,

so

`m=0.2 kg`

M=
`6*10^(24)` kg

`R=6.4*10^(6) m`

`G= 6.67*10^(-11) \ Nm^(2) kg-2`

As the gravitational force is existing among the earth and the apple

so

`F=(GMm)/(R^(2) )`

Putting the value of G,M,m and
`R^(2)`, we get

`(6.67*10^(-11) *6*10^(24) *0.2 )/((6.4*10^(6) )^(2) ) \\\\F= 1.9541\ N`

Consider a1 and a2 be a acceleration due to the gravitational force of earth attraction created on the apples

F= a1 *m

`a1\ =\ (F)/(m)`

a1=
`(1.9541)/(0.2)`

`a1=9.7705 \ m/s2`

Acceleration of the apple towards the earth is: 9.7705 m/s2.

again

`F= a2 *M`

a2=
`(F)/(M)`

`a2=( 1.9541)/(6**10^(24) ) \\a2=0.325* 10^(-24)\ m/s2`

So, Acceleration produced on earth towards the apple

`0.325*10^(-24) \ \ m/s2.`