The upper half of an inclined plane with inclination is perfectlysmooth while the lower halfis rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by

Step-by-step solution

Acceleration of block while sliding down upper half = g retardation of block while sliding down lower half =-( g - g ) For the block to come to rest at the bottom, acceleration in I half = retardation in II half. g =-( g - g ) =2 Alternative method: According to work-energy theorem, W = K =0 (Since initial and final speeds are zero) Work done by friction + Work done by gravity =0 i.e., -( mg ) 2 + mg =0 or 2 = or =2