The conditions for equilibrium of a system of coplanar parallel forces are as follows:

1. The vector sum (resultant) of all the forces acting on the system must be equal to zero. Mathematically, ΣF = 0, where ΣF represents the vector sum of all forces.
2. The algebraic sum of the moments (torques) of all the forces about any point in the plane must be equal to zero. This means that the sum of the clockwise moments must be equal to the sum of the counterclockwise moments. Mathematically, ΣM = 0, where ΣM represents the sum of moments or torques about a chosen point.

In the case of a meter rule balanced by a body at a particular position, let’s use the following variables:

• Length of the meter rule (L) = 100 cm (1 meter)
• Mass of the body (m) = 60 grams (0.06 kg)
• Position where the body is suspended (d) = 6 cm
• Position where the meter rule is balanced (P) = 48 cm

We need to ensure that the meter rule is in equilibrium. To do this, we must calculate the torque (moment) about the pivot point (usually the fulcrum), which in this case is P.

1. Calculate the torque due to the gravitational force acting on the body:

Torque (τ) = Force (F) × Distance (d) τ = m × g × d τ = 0.06 kg × 9.81 m/s² × 0.06 m τ = 0.03516 N·m (Newton-meters

In order to determine the conditions of equilibrium for a number of coplanar parallel forces acting on a meter rule, you need to consider the concept of moments or torques. For an object to be in equilibrium, the net torque (moment) acting on it should be zero. Here’s how you can apply this concept to the given scenario:

1. The meter rule is balanced at the 48 cm mark, which means the net torque about the pivot point (fulcrum) is zero. This implies that the sum of the clockwise moments equals the sum of the counterclockwise moments.
2. The body of mass 60g is suspended at the 6 cm mark, which will exert a downward force due to gravity (weight). To find the conditions of equilibrium, you should consider the forces and their respective distances from the pivot point:
   a. The weight of the body (mg), where m = 60g and g is the acceleration due to gravity (approximately 9.81 m/s²).
   b. The reaction force exerted by the meter rule at the 48 cm mark.
3. The conditions for equilibrium are as follows:
   Sum of clockwise moments = Sum of counterclockwise moments
   Mathematically, this can be expressed as:
   ΣM_clockwise = ΣM_counterclockwise
4. Now, you can calculate the moments (torques) of these forces:
   • Moment of the body’s weight (clockwise moment) = (0.06 kg) * (9.81 m/s²) * (6 cm / 100) m
   • Moment of the reaction force at the 48 cm mark (counterclockwise moment) = F_reaction * (48 cm / 100) m
5. Since the meter rule is balanced, ΣM_clockwise = ΣM_counterclockwise:
   (0.06 kg) * (9.81 m/s²) * (6 cm / 100) m = F_reaction * (48 cm / 100) m

Now, you can solve for the reaction force (F_reaction) at the 48 cm mark. Once you calculate F_reaction, you can verify if it satisfies the condition of equilibrium. If F_reaction equals the force due to the body’s weight, the system will be in equilibrium.