A block of mass m is released on a smooth movable inclined plane of inclination `30^(@)` and mass m. Height of the block varies with time as `h = 1.5 - 1.5 t^(2)` (h in meter and t = time in second). (all surfaces are smooth).

Options

A. Acceleration of inclined plane is `3sqrt(3) m//s^(2)`
B. Acceleration of blocks is `(3)/(2) sqrt(7)m//s^(2)`.
C. Acceleration of block with respect to inclined plane is `6 m//s^(2)`.
D. Acceleration of inclined plane is `(3sqrt(3))/(2) m//s^(2)`.

Answer

C, D

Explanation

`Tcostheta= mg`
`T sin theta = ma`
Solving `T = m sqrt(g^(2)+a^(2))" and "tantheta=(a)/(g)`
`mgsinalpha+T sin theta' = ma`
and `T'costheta = mg cosalpha`
Solving `T'=msqrt(g^(2)+a^(2)-2ag sin alpha)`
`tan theta = (a-g sintheta)/(g cos alpha)`