In the figure, the blocks A,B and C of mass m each have accelerations `a_(1),a_(2)` and `a_(3)` respectively. `F_(1)` and `F_(2)` are external forces of magnitude 2mg and mg respectively.

Options

A. `a_(1) = a_(2) = a_(3)`
B. `a_(1) gt a_(3) gt a_(2)`
C. `a_(1) = a_(2), a_(2) gt a_(3)`
D. `a_(1) gt a_(2), a_(2) = a_(3)`

Answer

D

Explanation

Extension in the spring is
`x = AB-R=2Rcos30^(@)-R=(sqrt(3)-1)R`
`therefore` Spring force
`F=kx=((sqrt(3)+1)mg)/(R)(sqrt(3)-1)R=2mg`
Free body diagram of bead is shown in figure.
`N=(F+mg)cos30^(@)=(2mg + mg)(sqrt(3))/(2)=(3sqrt(3)mg)/(2)`