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 value 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 friction forces on the block are equal.

Answer

A, B, C, D

Explanation

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