For the system shown in fig, there is no friction anywhere. Masses `m_(1) and m_(2)` can move up or down in the slots cut in mass M. Two non-zero horizontal force `F_(1)` and `F_(2)` are applied as shown. The pulleys are massles and frictionless. Given `m_(1) != m_(2)`

According to the above passage, which is correct?

Options

A. It is not possible for the entire system to be in equilibrium.
B. For some values `F_(1) and F_(2)`, it is possible that the entire system is in equilibrium.
C. It is possble that `F_(1)` and `F_(2)` are applied in such a way that `m_(1)` and `m_(2)` remain in equilibrium but M does not.
D. None of the above

Answer

A

Explanation

Let `m_(1)` and `m_(2)` do not accelerate up or down, then
`F_(1)=m_(1)g, F_(2)=m_(2)g`, but `m_(1) != m_(2)`, so `F_(1) != F_(2)`
Hence net horizontal force on M is `F_(1)-F_(2)`. So M cannot be in equilibrium. If M accelerates horizontally, then `m_(1)` and `m_(2)` also accelerated horizontally.