Question

Three identical masses are at the three corners of the triangle, connected by massless identical springs (rest length \( l_0 \)) forming an isosceles right angle triangle. If the two sides of equal length (of length \( 2l_0 \)) lie along the positive x-axis and positive y-axis, then the force on the mass that is not at the origin but on the x-axis is given by \( \hat{i} + \hat{j} \) with \( a \) and \( b \).

• A. \( a = 1 \) and \( b = 0 \)
• B. \( a = 0 \) and \( b = 1 \)
• C. \( a = -\sqrt{2} \) and \( b = 1 \)
• D. \( a = -2 \) and \( b = 0 \)
• E. \( a = -2 \) and \( b = 1 \)

Hint:

In problems involving springs, remember to use Hooke’s Law \( F = -k \Delta x \), where \( k \) is the spring constant and \( \Delta x \) is the displacement.

Answer 1

Answer: (E)

The system consists of three masses connected by identical springs. Using Hooke's Law, we can calculate the force on the mass at \( (x = 2l_0) \) on the x-axis.
Given that the force depends on the displacement and the spring constant, we determine the forces acting along the x and y axes. After solving the equations, we find that \( a = -2 \) and \( b = 1 \), which matches option (e).