A block of mass m is at rest relative to the stationary wedge of mass M. The coefficient of friction between block and wedge is `mu`. The wedge is now pulled horizontally with acceleration a as shown in figure. Then the minimum magnitude of a for the friction between block and wedge to be zero is:

Options

A. `gtantheta`
B. `mugtantheta`
C. `gcottheta`
D. `mugcottheta`

Answer

C

Explanation

The free body diagram of the block is as shown in the figure N is the normal reaction exerted by wedge on the block. The wedge moves towerds left with acceleration `a` then the component of acceleration of block normal to the plane is `a` `sintheta`. Applying newton's second law to the block normal to plane.
`mgcostheta-N=masintheta`
For N to be zero `a=gcottheta`
Hence the friction shall be zero when `a=gcottheta`.