Question

two objects one of mass 1 g and other of mass 1kg are dropped from the same height in vacuum. compare the two time intervals in which the two bodies will hit the ground

Answer 1

the objects will reach the ground at the same time even though one body weighs 1 gm and the other is 1 kg because in vaccum conditions there are no external forces acting on the bodies like air resistance

Answer 2

Given:

• Mass of the objects are 1 gram and 1 kg.

To find:

• Comparison between the two time intervals in which the bodies will hit the ground?

Calculation:

The general expression to calculate the time taken to reach the ground is :

$h = ut + \dfrac{1}{2} g {t}^{2}$

• Since, the object has been dropped, the initial velocity will be zero.

$\implies h = (0)t + \dfrac{1}{2} g {t}^{2}$

$\implies h = \dfrac{1}{2} g {t}^{2}$

$\implies {t}^{2} = \dfrac{2h}{g}$

$\implies t = \sqrt{\dfrac{2h}{g} }$

• Now, this equation is independent of mass of the object.

$\implies t \propto {m}^{0}$

So, both 1 gram and 1 kg object will reach the ground in same time.

• Hence, the ratio of the time interval taken by the bodies will be 1 : 1 .