Question

Two bodies of masses m₁ and m₂ fall from heights h₁ and h₂ respectively. The ratio of their velocities, when they hit the ground is
(a) $\frac{h_{1}}{h_{2}}$
(b) $\sqrt{\frac{h_{1}}{h_{2}}}$
(c) $\frac{m_{1}h_{1}}{m_{2}h_{2}}$
(d) $\frac{h_1 \ ^2}{{h_2\ ^2}}$

Answer 1

Velocity do not depends on mass

Answer 2

Answer:

Explanation:

In the case of a falling body, when an object falls from a height on the earth surface, before striking the earth's surface , the body only has  a  kinetic energy which is gained by losing the potential energy.  

Thus,

Kinetic energy at the bottom = potential energy at the top

K.E = P²/2m , where P is momentum and m is mass of body  

For the first body , K.E₁ = P₁²/2m₁

For the second body , K.E₂ = P₂²/2m₂

Potential energy of m₁ , P.E₁ = m₁gh₁

potential energy of m₂, P.E₂ = m₂gh₂  

Thus, ∵P.E = K.E  

Hence,

m₁gh₁ = P₁²/2m₁ and m₂gh₂ = P₂²/2m₂

P₁²/P₂² = m₁²h₁/m₂²h₂  

Square rooting both the sides,

P₁/P₂ = m₁/m₂√(h₁/h₂)