The maximum velocity and maximum acceleration of a particle executing SHM are 20 cm `s^(-1) and 100 cm s^(-2)`. The displacement of the particle from the mean position when its speed is 10 cm `s^(-1)` is

Options

A. 2 cm
B. 2.5 cm
C. `2sqrt(3) cm`
D. `2sqrt(2) cm`

Answer

C

Explanation

`V_(m)=Aomega=20cms^(-1)`
`a_(m)=Aomega^(2)=100cms^(-2)`
`(V_(m)^(2))/(a_(m))=A=(400)/(100)=4cm`
`(a_(m))/(V_(m))=omega=(100)/(20)=5" rad/s"`
`V=omegasqrt(A^(2)-y^(2)),10=5sqrt(4^(2)-y^(2))`
`4=4^(2)-y^(2),y^(2)=4^(2)-4=12,y=2sqrt(3)cm`