A planar object made up of a uniform square plate and four semicircular discs of the same thickness and material is being acted upon by four forces of equal magnitude as shown in Fig. The coordinates of point of application of forces is given by

Options

A. `(0,a)`
B. `(0,-a)`
C. `(a,0)`
D. `(-a,0)`

Answer

B

Explanation

The two forces along the y-direction balance each other. Hence the resultant force is `2F` along the `x`-direction. Let the point of application of the force be at `(0,y)`
(By symmetry, `x`-coordiate will be zero)
`F(a)+F(a)+F(a+y)-F(a-y)=0`
`implies y=-a`
Alternative method:
Torque will only be produced by the two forces acting along y-direction in anticlock direction. To balance this torque, we should apply a force `2F` in order to produce a torque in the clockwise direction, which is only possible if we apply a force at a point below the x-axis.
then `tau=F(a)+F(a)-2Fxxy=0`
`implies y=a`