A rigid rod of mass m3 is pivoted at point A, and masses m1 and m2 are hanging from it, as...

SKETCH:

The weights of the mass,and are pointed to the downward direction. We can take the point is the pivot point of the rod. It is shown in below figure.

RESEARCH:

The first condition for the static equilibrium:

The net force acting on the system must be zero when the system is in static equilibrium.

The second condition for the static equilibrium:

The net torque acting on the system about the pivot point must be zero when the system is in static equilibrium.

SIMPLIFY:

The torque due to weight of about the pivot point is given by

. . . . . . (1)

The torque due to weight of about the pivot point is given by

. . . . . . (2)

The torque due to weight of about the pivot point is given by

. . . . . . (3)

CALCULATE:

(a) Given that, the ratio of the weights of,, and is .

When the rigid rod is in static equilibrium then the net force acting on pivot point of the rod in y-direction must be equal to zero.

Therefore, the normal force acting on the pivot point is given by

(b) When the rod is in static equilibrium, then the net torque acting on the rod about the pivot point must be zero.

Substitute the equations (1), (2) and (3) are in above equation, we get

Then the ratio between the distance from the pivot point to and the distance from the pivot point to can be calculated as