Q1: The necessary condition of equilibrium of a body, is :

ANS:D - all (a), (b) and (c).

(a) Algebraic sum of horizontal components of all the forces must be zero: When a body is in equilibrium, the sum of all the forces acting on it in the horizontal direction must be zero. This means that if you add up the horizontal components of all the forces (considering their directions and magnitudes), the result should be zero. In other words, the forces pushing or pulling the object from left to right must balance out with the forces pushing or pulling it from right to left. (b) Algebraic sum of vertical components of all the forces must be zero: Similar to the horizontal condition, in the vertical direction, when a body is in equilibrium, the sum of all the forces acting on it vertically must be zero. This implies that the upward forces must balance out the downward forces. (c) Algebraic sum of the moments of the forces about a point must be zero: When a body is in rotational equilibrium (or equilibrium with respect to rotation), the sum of the moments (torques) of all the forces acting on it about any chosen point must be zero. This is based on the principle of rotational equilibrium, where the torque about any point is the product of the force and the perpendicular distance from the point to the line of action of the force. For an object to remain in rotational equilibrium, the clockwise and counterclockwise moments around any point must balance each other out.