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Motion under gravity and time of fall

A body of mass m1 and another body of mass m2 are dropped from wqual heights.If time taken by the balls are t1 and t2 respectively then t1=t2. How ?

The acceleration due to gravity is independent of mass of body. When two different masses  are dropped from the  same height, they will take same time  to reach the surface of earth.

Pendulum on Mount Everest !

If you set a pendulum atop Mt. Everest, would the period be less than, greater than or equal to the period you would get in the lab?  Explain.

Ans:

As you know, the acceleration due to gravity decreases as we go upwards from surface of earth.

The time period of a simple pendulum is given by

Where l is the length of the pendulum, and g is the acceleration due to gravity.

From the equation, we can conclude that, the Time period of the pendulum increases (i.e. it goes slower)  if the pendulum is set up on top of Mount Everest.

For Creative and Critical Thinkers

Here we have not considered the change in temperature between the laboratory conditions and the temperature on top of Mount Everest which is very low. A decrease in temperature would decrease the length of the pendulum (Unless it is made up of such a substance which does not change its length with change in  temperature) and will also decrease the time period of the pendulum, making it move faster.

My first answer is correct only if the laboratory conditions are the same as on top of Mt. Everest or vice versa, except for the difference in altitude (height)