For a body in `SHM` the velocity is given by the relation `V = sqrt(144-16x^(2))ms^(-1)`. The maximum acceleration is

Options

A. 12 `m//s^(2)`
B. 16 `m//s^(2)`
C. 36 `m//s^(2)`
D. 48 `m//s^(2)`

Answer

D

Explanation

`V = sqrt(144 - 16x^(2))" "V = 4 sqrt(9-x^(2))`
by comparing with `V = omega sqrt(A^(2) - x^(2))`
we get `omega = 4, A = 3`
`a_(max) = omega^(2) A = 16 xx 3 = 48`