Q. 375.0( 1 Vote )

(a) With the help of Second Law of Motion and the Universal Law of Gravitation derive an expression for acceleration due to gravity ‘g’.

(b) The weight of any person on the moon is about 1/6 times that on the earth. He can lift a mass of 15 kg on the earth. What will be the maximum, mass, which can be lifted by the same force applied by the person on the moon?

OR

(a) Identical packets are dropped from two aeroplanes, one above the equator and the other above the north pole, both at height ‘h’. Assuming all conditions are identical, will these packets take same time to reach the surface of the earth? Justify your answer.

(b) It is seen that a falling apple is attracted towards the earth. Does the apple also attract the earth? If so, we do not see the earth moving towards the apple. Why?

Answer :

(a) Consider an object of mass m lying on or near the surface of the Earth. Let Me be the mass of the Earth and Re be its radius i.e., Re is the distance between the object and the centre of the Earth.


According to Newton's law of gravitation, the force of attraction (F) between the Earth and the object is-


------ (1)


According to Newton's second law of motion this force produces an acceleration (g) in the object.


F = ma (a = g)


F = mg


g = F/m -------- (2)


Substituting the value of F in eq (2) we get


g =


g = -------- (3)


From eq (3) it is very clear that acceleration due to gravity does not depend on the mass m of the object. It only depends on the mass of the Earth (Me) and the distance from the centre of the Earth to the object.


(b) Gravity on earth ge= g


Gravity on moon gm= g/6


Thus, force applied to lift a mass of 15kg on the earth is, F=mge


= 15 g N


Mass lifted by the same force on the moon is,



m =


m =15× 6 = 90 kg


OR


(a) The value of acceleration due to gravity varies from one place to another on the surface of earth, because earth is not a perfect sphere, is flattened at the poles and bulged out at the equators. The value of g at the equator is less than the value of g at the north pole. Hence the packet will be fall slowly at the equator in comparison to the North pole. Thus the packet dropped above the equator will take longer to reach the surface of the earth.


(b) The earth attracts an apple and so does the apple attracts the earth with an equal and opposite force. Mass of the earth is extremely massive as compared to the mass of moon. So, the acceleration produced is very small as compared to that in the apple. Hence, the motion of the earth towards the apple is not noticeable.


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