A cubical block of mass `m` is sliding on an inclined right angle trough as shown in the figure. If coefficient of friction is `mu` , find the acceleration of the block.

Explanation

For the cubical block , `N_(1) = N_(2) = N`
Resultant reaction `N' = sqrt(2) N`
`_|_^(ar) to JK : N' mg cos theta rArr sqrt(2) N = mg cos theta`
`rArr N = (mg cos theta)/(sqrt(2))`
Along the plane : `mg sin theta - mu N_(1) - mu N_(2) = ma`
`mg sin theta - 2 mu N = ma`
`mg sin theta - 2 mu (mg cos theta)/(sqrt(2)) = ma`
` a = g[ sin theta - sqrt(2) mu cos theta]`