A block of mass `2kg` slides down the face of a smooth `45^@` wedge of mass `9 kg` as shown in the figure. The wedge is placed on a frictionless horizontal surface. Determine the acceleration of the wedge.

Options

A. `2m//s^(2)`
B. `(11)/(sqrt2)m//s^(2)`
C. `1m//s^(2)`
D. none of these

Answer

C

Explanation

a is acceleration of block w.r.t. wedge.
For block:
`N+mAsin45^(@)=mgcos45^(@)`
For wedge: `Nsin45^(@)=MA`
From (i) and (ii) `A=1m//s^(2)` .