The block of mass `m` is being pulled by a horizontal force `F=2`mg applied to a string as shown in figure (Take `g=10(m)/(s^2)`). The pulley is massless and is fixed at the edge of an immovable table. What is the value of force exerted by the supporting table on the pulley (in Newton)

Options

A. `3 mg`
B. `4 mg`
C. `2sqrt(2) mg`
D. `2 mg`

Answer

C

Explanation

The F.B.D of pulley is as shown

Let `vec(T)_(1),vec(T)_(2)` and `vec(F)_(S)` be the forces exerted by the horizontal string, vertical string and the support on the massless pulley respectively Then
`vec(T)_(1)+vec(T)_(2)+vec(F)_(S)=0`
or `|vec(F)_(S)|=|vec(T)_(1)+vec(T)_(2)|=2 sqrt(2)mg`
(Tension in each string is `|vec(T)_(1) |=| vec(T)_(2)|=2 mg`)
`2 sqrt(2) mg`.