Question

The upper half of an inclined plain of inclination theta is perfectly smooth while lower half is rough a block starting from rest at the top of the plane will again come to rest at the bottom if the coefficient of frictikn between the block and lower half of plane is given by

Answer 1

it should be 2tanθ... let the friction coffecient of lower half be μ ...length of inclination be 2δ so the height of wedge containing incline will be 2δsinθ for upper half.. u may simply apply energy conservation and u will get velocity at mid point of incline =√2gδsinθ ...then for lower half use ''total work done =Δk.e'' from here u will get
mgδsinθ – μmgδcosθ= 0 – (½)2mgδsinθ {∵v=√2gδsinθ.. and final k.e of block will be 0 as it will come in rest}
μ=2tanθ..
hope it helped.. mark brainliest