An apple of mass `0.25` kg falls from a tree . What is the acceleration of the apple towards the earth ? Also calculate the acceleration of the earth towards the apple . Mass of the earth = `5.983 xx 10^(24)` kg , Radius of the earth = `6.378 xx 10^(6)` m and G = `6.67 xx 10^(-11)Nm^(2) kg^(-2)`

Options

A. `2xx10^(-25)m//s^(2)`
B. `4xx10^(-25)m//s^(2)`
C. `3.1xx10^(-20)m//s^(2)`
D. `8.5xx10^(-20)m//s^(2)`

Answer

B

Explanation

The gravitational force between the earth and the apple is
`F=(GMm)/(R^(2))`
`therefore` Acceleration of the earth towards the apple
`a=(F)/(M)=(GMm)/(R^(2)xx M)=(Gm)/(R^(2))`
`= (6.67xx10^(-11)xx0.25)/((6.4xx10^(6))^(2))`
`a div 4xx10^(-25)m//s^(2)`