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Question

Two bodies of different masses ma and mb are dropped from two different heights a and b. The ratio of the time taken by the two to cover these distances are


A

a:b

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B

b:a

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C

a:b

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D

a2:b2

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Solution

The correct option is C

a:b


We know initial velocity, u of both the bodies is zero.
Using equation of motion, S=ut+12at2
where, S= height of the bodies(h), u=0, a= acceleration due to gravity(g) and t= time period.
we have,

h=12gt2

t=2hg
Let time for body 'a' be ta and time for body 'b' be tb.
Given, height of 'a'= a and height of 'b'= b.

For the two bodies in question, we have

ta=2ag and tb=2bg

tatb=ab


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