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

`(B)` The two forces along `y-` direction balance each other.
Hence, the resultant force is `2F` along `x-` direction
Let the point of application of force be at `(0,y)`.
`(` By symmetry `x-` coordinate with be zero `)`.
For rotational equilibrium `:`
`F(a)+F(a)+F(a+y)-F(a-y)=0`
`rArr y=-a ` Hence `(B)`.
`F(a)+F(a)+F(a+y)-F(a-y)=0`
`rArr y=-a ` Hence `(B)`.
Alternate `:`
Torque will only be produced by the two forces along `y-` direction in anti`-` clockwise 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`
`rArr y=a` Hence `(B)`.