Question

time taken by an object falling from rest to cover the height of H1 and H2 is respectively T1 and t2 then the ratio of T1 to T2

Answer 1

from the principle of conservation of energy

potential energy = kinetic energy

or

(1/2)mv2 = mgh

or

v = √(2gh)

 

so, the velocity of the two bodies would be

v1 = √(2gh1)

and

v2 = √(2gh2)

 

the ratio of the velocities would be

v1/v2 = √(h1) / (√h2)

 

so, the correct answer would be option (a).

 

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Answer 2

H1=ut+1/2gt1^2
H1=1/2gt1^2
T1= √2H1/g (1) eq

H2=ut+1/2gt2^2
H2=1/2gt2^2
T2=√2H2/g

T1/T2=√2H1/g/√2H2/g
T1/T2 = H1/H2