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`.

Options

A. `10 m//s^(2)`
B. `5 m//s^(2)`
C. `20 m//s^(2)`
D. `1 m//s^(2)`

Answer

A

Explanation

Let `a_(0)` : acceleration of the block with respect to the disc
`ma cos theta - mu N_(1) - mu N_(2) = ma_(0)`
`ma cos theta - mu mg - mu mg - mu ma sin theta = ma_(0)`
`a_(0) = a cos theta - mu g - mu a sin theta`
`= 25 xx (4)/(5) - (2)/(5) xx 10 - (2)/(5) xx 15 xx (3)/(5)`
` = 20 - 4 - 6 = 10 m//s^(2)`