Consider a system of blocks X, A and B as shown in the figure. The blocks A and B have equal mass and are connected by a massless string through a massless pully. The coefficient of driction between block A and X or B and X is 0.5. If block X moves on the horizontal frictionless surface what should be its minimum acceleration such that blocks A and B remain stationary. (g = acceleration due to gravity.)

Options

A. `g/3`
B. `3g`
C. `g/4`
D. `(3g)/4`

Answer

A

Explanation

Given, Mass of block A and B, `m_(A)=m_(B)=m`. Coefficient of friction between each block and surface, `mu=0.5`.

Block X moves with acceleration a such that block A and B remains stationary. Block B is stationary only when, Tension force on block B is equal to friction force on B.
i.e., `T= mu R`
`T= mu m a` ...(i) `[ :' R= ma ]`
Block A is stationary only when friction force on block A is equal to the sum of tension force on block A and applied force on block A.
`muR=T+ma`
`mu mg=mu m a +ma` [From Eq. (i)]
`mu g=mu a+a`
`mu g =a(mu +1)`
`a=( mu g)/( mu+1)=(0.5 g)/(0.5 +1)=(0.5 g)/1.5=g/3`
`:. a=g/3`
Thus, `g//3` should be its minimum acceleration such that block A and B remains stationary.