Three different objects of masses $m_{1}, m_{2} a n d m_{3}$ are made to fall from rest along three frictionless paths, from the same height. What is the ratio of their speeds to reach the ground?

$1 : 1 : 1$

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$3 : 2 : 1$

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$\frac{1}{m_{1}} : \frac{1}{m_{2}} : \frac{1}{m_{3}}$

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$1 : 2 : 3$

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Solution

The correct option is A
$1 : 1 : 1$

As there is no loss of energy due to friction, the energy remains conserved. i.e., the potential energy of all the masses gets converted to their kinetic energy. Thus, all the masses have velocity, which is equal to :
$m \times g \times h = \frac{1}{2} \times m \times v^{2}$
$v = (2 g h)^{\frac{- 1}{2}} .$

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Three different objects of masses m1,m2 and m3 are made to fall from rest along three frictionless paths, from the same height. What is the ratio of their speeds to reach the ground?

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