A particle moves in a plane along an elliptic path given by `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` At point (0, b), the x-component of velocity is u. The y-component of acceleration at this point is-

Options

A. `-(bu)^(2)/a^(2)`
B. `-u^(2)/b`
C. `-(au)^(2)/b^(2)`
D. `-u^(2)/a`

Answer

A

Explanation

`x^(2)/a^(2) + y^(2)/b^(2) =1`
`u_(x)= u` [At (0,b)]
`u_(y) = 0`
`(2x)/y^(2) .(dx)/(dt) + (2y)/(b)^(2).(dy)/(dt)=0`
Again diff. Wr.t. to time
`(2x)/a^(2).(d^(2)x)/(dt^(2)) + 2/a^(2) ((dx)/(dt))^(2) + (2y)/b^(2).(d^(2)y)/(dt^(2)) + 2/b^(2) ((dy)/(dt))^(2) =0`
`rArr 0 + 2/a^(2)u^(2) + 2/b a_(y) + 0 = 0` [At (0,b)]
y - component of acceleration at (0,b) is `a_(y) = -b/a^(2)u^(2)`