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)P`
B. `(III)(iii)Q`
C. `(IV)(i)Q`
D. `(II)(iii)(R )`

Answer

C

Explanation

For block to move `mu lt tan theta implies mult1……(i)`
For wedge to move
`(N)/(sqrt(2))-(muN)/(sqrt(2))lt mu N'`
`mu lt sqrt(5)-2" "....(ii)`
Work done by kenetic friction on block and wedge is negative.