To determine the reading of the dynamometer in this scenario, we need to analyze the forces acting on the two masses, M and m, and how they interact through the dynamometer. The setup involves two forces applied in opposite directions, and the dynamometer measures the tension in the connecting string or cable. Let's break this down step by step.
Understanding the Forces at Play
In the given problem, we have:
- Mass M = 6 kg, with a force F1 = 20 N acting to the left.
- Mass m = 4 kg, with a force F2 = 10 N acting to the right.
Calculating the Net Force
The first step is to calculate the net force acting on the system. Since the forces are applied in opposite directions, we can find the resultant force by subtracting the smaller force from the larger force:
Net Force (F_net) = F1 - F2 = 20 N - 10 N = 10 N
Analyzing the System
Now, we need to consider how this net force affects the reading on the dynamometer. The dynamometer measures the tension in the string connecting the two masses. When the larger force (20 N) is applied to mass M, it will try to accelerate both masses. However, the smaller force (10 N) acting on mass m will resist this acceleration.
Determining the Acceleration
To find the acceleration of the system, we can use Newton's second law, which states that:
F = ma
Here, the total mass of the system is:
Total Mass (M_total) = M + m = 6 kg + 4 kg = 10 kg
Now, we can calculate the acceleration (a) of the system:
a = F_net / M_total = 10 N / 10 kg = 1 m/s²
Finding the Tension in the String
Next, we need to find the tension in the string, which is what the dynamometer reads. The tension (T) can be calculated by considering the forces acting on either mass. Let's analyze mass m (4 kg) since it has the smaller force acting on it:
For mass m, the forces acting on it are the tension in the string (T) and the applied force (F2 = 10 N). According to Newton's second law:
F2 - T = m * a
Substituting the known values:
10 N - T = 4 kg * 1 m/s²
10 N - T = 4 N
Now, solving for T:
T = 10 N - 4 N = 6 N
Final Reading of the Dynamometer
Thus, the reading of the dynamometer, which measures the tension in the string, will be:
6 N
Therefore, the correct answer is (C) 6 N. This analysis shows how the forces interact and how the tension in the system can be calculated using basic principles of physics.
