Three different objects of masses m_1, m_2 an | vedclass

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Question

(C) According to the law of conservation of energy,the potential energy at the top is converted into kinetic energy at the bottom.$mgh = \frac{1}{2}mv

Vedclass · Accepted Answer

$1 : 1 : 1$

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(C) According to the law of conservation of energy,the potential energy at the top is converted into kinetic energy at the bottom.$mgh = \frac{1}{2}mv^2$Here,$m$ is the mass of the object,$g$ is the acceleration due to gravity,$h$ is the height,and $v$ is the final velocity.Canceling $m$ from both sides,we get $gh = \frac{1}{2}v^2$,which simplifies to $v = \sqrt{2gh}$.Since all three objects fall from the same height $h$ and are subject to the same acceleration due to gravity $g$,their final speeds will be independent of their masses.Therefore,the ratio of their speeds is $v_1 : v_2 : v_3 = \sqrt{2gh} : \sqrt{2gh} : \sqrt{2gh} = 1 : 1 : 1$.

Three different objects of masses $m_1, m_2$ and $m_3$ are allowed to fall from rest and from the same point $O$ along three different frictionless paths. The speeds of the three objects,on reaching the ground,will be in the ratio of

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