A particle moves along a straight line to follow the equation `ax^(2) + bv^(2) = k`, where `a, b` is and k are constant and `x` and and `x` axis coordirete and velocity of the particle respectively find the amplitude

Options

A. `sqrt((k)/(b))`
B. `sqrt((b)/(k))`
C. `sqrt((a)/(k))`
D. `sqrt((g)/(a))`

Answer

D

Explanation

`ax^(2) + bv^(2) = k`
`hv^(2) = k - ax^(2)`
`v^(2) = (k)/(b) - (a)/(b) x^(2)`
Compare with `v^(2) = A^(2) omega^(2) - omega^(2)x^(2)`
`omega^(2) = d//b` and `A^(2)omega^(2) = k//b`
`A = sqrt((A^(2) omega^(2))/(omega^(2)) = sqrt((k//b)/(a//b)) = sqrt((k)/(a))`