In the arrangement shown below..m1 = 1kg and m2 = 2kg.Pulleys are massless and the strings are light.What value of M the mass m1 moves with constant velocity.Neglect friction.

To determine the value of mass M that allows mass m1 (1 kg) to move with constant velocity, we need to analyze the forces acting on both masses in the system. Since the pulleys are massless and the strings are light, we can apply Newton's laws of motion to find the equilibrium condition for m1.

Understanding the Forces

When m1 is moving with constant velocity, it means that the net force acting on it is zero. This occurs when the gravitational force acting on m1 is balanced by the tension in the string caused by the weight of mass M. Let's break down the forces involved:

• Weight of m1: The force due to gravity acting on m1 is given by F1 = m1 * g, where g is the acceleration due to gravity (approximately 9.81 m/s²). For m1 = 1 kg, this force is:
• Weight of m2: The force due to gravity acting on m2 (which is M) is F2 = M * g.

Setting Up the Equation

Since m1 is moving with constant velocity, we set the forces equal to each other:

F1 = F2

Substituting the expressions for the forces, we have:

m1 * g = M * g

Simplifying the Equation

We can simplify this equation by canceling out g from both sides (assuming g is not zero):

m1 = M

Now, substituting the value of m1:

1 kg = M

Conclusion

Thus, for mass m1 (1 kg) to move with constant velocity, the mass M must also be 1 kg. This balance ensures that the forces acting on m1 are equal and opposite, resulting in no net acceleration. In practical terms, if M were greater than 1 kg, m1 would accelerate downward, and if M were less than 1 kg, m1 would accelerate upward. Therefore, maintaining M at 1 kg keeps the system in equilibrium, allowing m1 to move steadily.