Question

The spheres A and B as shown have mass M each.
The strings SA and AB are light and inextensible
with tensions 7 and 7 respectively. A constant
horizontal force F =Mg is acting on B. For the
system to be in equilibrium we have​

Answer 1

Explanation:

From Figure, the gravitational force on mass 2m at G due to mass at A is

F1=G12m×2m=2Gm2 along GA

Gravitational force on mass 2m at G due to mass at B is

F2=G12m×2m=2Gm2 along BG

Gravitational force on mass 2m at G due to mass at C is F3=G12m×2m=2Gm2 along GC

Draw DE parallel to BC passing through point G. Then ∠EGC=30o=∠DGB.

Resolving F2 and F3 into two rectangular components, we have

F2cos30o along GD and F2sin30o along GH

F3cos30o along GE and F2sin30o along GH

Here, F2cos30o and F3sin30o are equal in magnitude and acting in opposite directions, and cancel out each other. The resultant force on mass 2m at G is

F1