In the figure shown , A and B are free of to move. All the surfaces are smooth. `(0 lt theta lt 90^(@))`

Options

A. the acceleration of A will be more than `g sin theta`
B. the acceleration of A will be less than `g sin theta`
C. normal force on A due to B will be more than `mg cos theta`
D. normal force on A due to B will be less than `mg cos theta`

Answer

`A, D`

Explanation

`ma_(0)sintheta+N=mg costheta rArr N=mgcostheta=ma_(0)sintheta`
`rArr Nltmg costheta`
Hence, (D) is ture.
`ma_(0)costheta+mg sintheta=ma`
`rArr a=g sintheta+a_(0) costheta`
Hence acceleration of `A`
`=sqrt((a-a_(0)costheta)^(2)+(a_(0)sintheta)^(2))gtg sin theta`