an apple with mass of 200 grams falls from a tree towards the earth.calculate the acceleration towards the earth and also calculate the acceleration of earth towards it
Answers
Answer:
Here, Mass of apple (m) = 200 g = 200/1000 kg = 0.2 kg
Mass of the earth (M) = 6×1024 kg
Radius of Earth (R) = 6.4×106 m
Universal gravitational constant (G) = 6.67×10-11 Nm2kg-2
In this question, apple falls from tree to the surface of earth. Here, an apple and the earth are considered as two masses attracting each other. You know the radius of an apple is very small so it is negligible as compared to the radius of the earth. The distance between earth and an apple is nearly equal to the radius of the earth because the distance from surface of earth to center of an Apple is very small as compared to radius of the earth. We know, according to Newton's law of gravitation, two masses attracts each other; earth pulls an apple towards its center and apple pulls earth towards its center by equal force.
Thus, the gravitational force existing between the earth and an apple (F) = GMm/R2.
or, F= (6.67×10-11×6×1024×0.2)/( 6.4×106)2
or, F= (8.004 × 1013)/(40.96×1012)
or, F= 0.19541×1013-12
or, F= 1.9541 N
If earth attracts apple towards it then there may be acceleration produced while falling towards center of earth. Let a1 be the acceleration produced on apple due to gravitational force of attraction of earth, then
F= ma1
or, a1 = F/m
or, a1 = 1.9541/0.2
or, a1 = 9.7705 m/s2
Therefore, the acceleration of an apple towards the earth is 9.7705 m/s2.
Similarly, an apple attracts earth towards its center with force 1.9541 N. Let a2 be the acceleration produced on the earth towards apple, then
F=Ma2
or, a2= F/M
or, a2 = 1.9541/6×1024
or, a2 = 0.325×10-24 m/s2
Therefore, acceleration produced on earth towards an apple is 0.325×10-24 m/s2.
Here, the value of acceleration produced on an apple is 9.7705 m/s2 and the acceleration produced on earth is 0.325×10-24 m/s2. The acceleration produced on an earth is very small so it is not detectable. That’s why, we do not see the earth moving towards an apple.