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A particle is thrown vertically upwards from the surface of the earth. Let Tp be the time taken by the particle to travel from a point P above the earth to its hightst point and back to P. Similarly let Tq be the time taken by the particle to travel from a point Q above the earth to its hightst point and back to Q. If the distance between the points P and Q is H then find the expression of acceleration due to gravity in terms of Tp, Tq and H .

Purva , 6 Years ago

Grade 11

1 Answers

Eshan

Last Activity: 6 Years ago

Dear student,

Let the speed of particle at P and Q points be $v_P$ and $v_Q$ , respectively. Hence

$T_P=\dfrac{2v_P}{g}$ and $T_Q=\dfrac{2v_Q}{g}$

From the equation of motion,

$v_P^2-v_Q^2=2gH$
$\implies \dfrac{g^2T_P^2}{4}-\dfrac{g^2T_Q^2}{4}=2gH\implies g=\dfrac{8H}{T_P^2-T_Q^2}$

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