A circular disc with a groove along its diameter is placed horizontally on a rough surface. A block of mass 1 kg is placed as shown. The co-efficient of friction between the block and all surfaces of groove and horizontal surface in contact is `mu=2/5`. The disc has an acceleration of `25m//s^2` towards left. Find the acceleration of the block with respect to disc. Given `cos theta=4/5`, `sin theta=3/5`.

Answer

10

Explanation

Applying pseudo force ma and resolving it along and normal to groove.
Applying along the groove
`m a cos theta - (f_(1) + f_(2)) = ma_(x)`
`m a cos theta - mu N_(2) - mu N_(2) = ma_(x)`
`ma cos theta - mu m a sin theta - mu m g = ma_(x)`
`a_(x) = a cos theta - mu a sin theta - mu g`
`= 25 xx (4)/(5) - (2)/(5) xx 25 xx (3)/(5) - (2)/(5) xx 10 = 10 m//s^(2)`