2004 AIPMT Work, Energy and PowerKinetic Energy in Free Fall Easy Question 63 of 71 in Work, Energy and Power

A ball of mass 2 kg and another of mass 4 kg are dropped together from a 60 feet tall building. After a fall of 30 feet each towards earth, their respective kinetic energies will be in the ratio of-

A 1 : 4
B 1 : 2
C $1 : \sqrt{2}$
D $\sqrt{2} : 1$

The answer is B.

Solution

Both balls are dropped from rest and fall the same height h = 30 ft. In free fall the velocity does not depend on mass.
Here $v_1 = v_2 = \sqrt{2gh}$
$\dfrac{KE_1}{KE_2} = \dfrac{\frac{1}{2}m_1v_1^2}{\frac{1}{2}m_2v_2^2} = \dfrac{m_1}{m_2}$
$= \dfrac{2}{4} = \dfrac{1}{2}$
So their kinetic energies are in the ratio 1 : 2.

Concept KE proportional to mass at equal velocity

Work, Energy and Power in past papers

71 questions from this chapter have appeared across 27 exam years.