To solve this problem, we need to analyze the forces acting on the blocks and their subsequent accelerations.
Given:
- Mass of Block A = 1 kg
- Mass of Block B = 4 kg
- Mass of Block C = 2 kg
- Total mass of the system = \(1 + 4 + 2 = 7 , \text{kg}\)
If the acceleration of the system is \(5P\) ms² and \(P = 2\), then: \[ a = 5 \times 2 = 10 , \text{ms}^{-2} \]
To find the net force acting on the system, we can use Newton's second law, which states that the net force \(F\) is equal to the mass \(m\) multiplied by the acceleration \(a\):
\[ F = ma \]
Substituting in the total mass of the blocks and the calculated acceleration:
\[ F = 7 , \text{kg} \times 10 , \text{ms}^{-2} = 70 , \text{N} \]
So, the net force required to accelerate the system is \(70 , \text{N}\).
If there are external forces acting on the blocks or if they are connected in some way (elastic bands, ropes, etc.), further analysis of the forces would be required. However, from the information given, we concluded that with an acceleration of \(10 , \text{ms}^{-2}\) for the total mass of \(7 , \text{kg}\), the net force is indeed \(70 , \text{N}\).
In conclusion, the value of P is indeed \(2\) as stated.