The figure shows a smooth fixed wedge on which a block of mass m is kept and released, then which of the following (s) are true.
(`vec(a) =` acceleration of block and N is the contact force between the block and the wedge)

Options

A. `N cos theta = mg`
B. `N = mg cos theta`
C. `vec(a) = (N sin theta hat(i))/(m) + ((N cos theta - mg)/(m)) hat(j)`
D. `vec(a) = g sin theta cos theta hat(i) - g sin^(2) theta hat(j)`

Answer

B, C, D

Explanation

`N = mg cos theta`
`a = g sin theta` or
`vec(a) = (N sin theta)/(m) hat(i) + ((N cos theta - mg) hat(j))/(m)`
`vec(a) = g sin theta cos hat(i) + g sin^(2) theta (-hat(j))`