Release a single molecule in an evacuated region and it will fall as fast as, and no differently from, a baseball released in the same region. Explain.
Solution 32E Step 1: Consider the mass of the molecule as “m”. If it is allowed to fall freely in an evacuated region, the only force experiencing is the gravitational force. 2 According to Newton’s universal law of gravitation, F = GMm/r Where, G - Gravitational constant M - Mass of earth (if the object is attracted by earth) m - mass of the molecule r - Distance between the earth and the molecule But we know that, force, F = ma from Newton’s 2nd law of motion. Where “m” is the mass of the molecule and “a” acceleration of the molecule under the influence of the force. So, replacing ‘F’ as ‘ma’ in the equation for gravitational force we get, ma = GMm/r 2 ‘m’ will cancel out on both sides and we get, a = GM/r which is a constant. So, the acceleration here is nothing but acceleration due to gravity and it will be a constant for earth. If we repeat the same process by using the mass of a baseball, it will not be changed and it is a constant. The acceleration due to gravity is represented by using the letter ‘g’. Since the acceleration is a constant, it does not depend on the mass of the falling object. If two objects are released from same height, both of them will reach the ground at same time. But, there is a possibility for the frictional force due to air. Actually the air resistance influences the free fall of objects with different masses. Conclusion: In this case, since the region is evacuated, the molecule and baseball released from the same height will hit the ground at same time since the acceleration due to gravity is same.