In the adjacent figure blocks A and B of weight W each are lying at rest on a rough horizontal surface. They are pulled by applying forces `F_(1)` and `F_(2)` as shown in figure. When blocks are in limiting equilibrium `F_(2)=5F_(1)` Choose the correct statement (s) (Assume same coefficient of friction for both the blocks)

Options

A. The value of frictional force on the block B is equal to five time the vlaue of frictional force on A.
B. the coefficient of friction is equal to `(8)/(9)`
C. The ratio of `F_(1)` to the weight of the block W (i.e., `(F_(1))/(W)`) is equal to `(2)/(3)`
D. The value of frictional forces on the block are equal.

Answer

A, B, C

Explanation

For block A
`F_(1)cos37^(@)=muN_(1)` .(i)
`N_(1)=W-F_(1)sin37^(@)` .(ii)
For block B
`5F_(1)cos37^(@)=muN_(2)` .(iii)
`N_(2)=W+5F_(1)sin37^(@)` .(iv)
from (i) & (ii)
`(4F_(1))/(5)+muxx(3F_(1))/(5)=muW`
(iii) & (iv)
`4F_(1)-mu3F_(1)=muW`
On solving `mu=(8)/(9)` and `(F_(1))/(W)=(2)/(3)`