Two wedges, each of mass `m`, are placed next to each other on a flat horizontal floor. A cube of mass `M` is balanced on the wedges as shown in figure. Assume no friction between the cube and the wedges, but a coefficent of static friction `mult1` between the wedges and the floor. What is the largest `M` that can be balanced as shown without motion of the wedges ?

Options

A. `(m)/(sqrt(2))`
B. `(mu m)/(sqrt(2))`
C. `(mu m)/(1-mu)`
D. `(2 mu m)/(1-mu)`

Answer

D

Explanation

The free body diagrams of all bodies are as shown.

From `FBD` of blcok
`2N cos 45^(@)=Mg ……(1)`
For wedge to remain at rest
`N sin 45^(@) lt mu N' ……(2)`
and `N' =mg+N cos 45^(@) ….(3)`
From `1,2, ` and 3 we get
`Mle(2mum)/(1-mu)`