In the figure shown, if friction coefficient of block 1 kg and 2kg with inclined plane is `mu_(1) = 0.5` and `mu_(2) = 0.4` respectively, then

Options

A. both block will move together
B. both block will move separately
C. there is a non-zero contact force between two blocks
D. none of these

Answer

B

Explanation

If we consider blocks 2 & 1 independently then there acceleration would be for block (A)
`a_(1)=g sin theta -mu_(1)g cos theta =g`
`[(sqrt(3))/(2)-(1)/(2)xx(1)/(2)]=(g[2 sqrt(3)-1])/(4)`
for block (B)
`a_(2)=g sin theta -mu_(2) gcos theta =g`
`[(sqrt(3))/(2)-(2)/(5)xx(1)/(2)]=(g)/(10)[5 sqrt(3)-2]`
`sin a_(2) gt a_(1)` so both blocks will move separately.