A block is released on the slant face of a wedge of equal mass placed on a horizontal floor. The slant face of the wedge makes an angle of `45^(@)` with the floor. Coefficient of friction between all surfaces in contact is the same. Different value/ range of coefficient of friction is given in column I and corresponding consequences in column II and III (wedge is fress to move)

`{:(,"Column-I",,"Column-II",,"Column-III",),((I),mu=0,(i),"Work done by friction on block and wedge is negative (on each)",(P),"Centre of mass of system (block+wedge) moves rightward and downward",),((II),mu gt 1,(ii),"Work done by friction on block is negative but on wedge it is zero",(Q),"Centre of mass of system (block+wedge) moves leftward and downward",),((III),sqrt(5)-2 lt mu lt 1,(iii),"Work done by friction on block and wedge is zero (on each)",(R ),"Centre of mass of system (block+wedge) remains at rest",),((IV),mu lt sqrt(5) - 2,(iv),"Friction between the block and wedge is static and between the wedge and ground it is kinetic in nature.",(S),"Centre of mass of system (block+wedge) moves vertically downward",):}`
Which of the following options is the correct representation of the case that the wedge remains motionless and the block slides down

Options

A. `(I) (iv)S`
B. `(III)(ii)Q`
C. `(IV)(i)Q`
D. `(II)(iii)R`

Answer

B

Explanation

Block moves if `multtantheta`
`implies mult1 " ".....(i)`

For the wedge not to move
`(N)/sqrt(2)-(muN)/sqrt(2)lemuN'`
Here `N=(mg)/sqrt(2)" " N'=(muN)/sqrt(2)+(N)/sqrt(2)+mg`
`"therefore" " "mu ge(sqrt(5-2))" ".....(ii)`
So`(sqrt(5-2))lemu lt1`
Work done by friction on wedge is zero and on block it is negative.