Question

An iron block A of volume \( 0.25\ \text{m}^3 \) stretches a spring by 0.2 m. A new block B of volume \( 0.75\ \text{m}^3 \) is kept on a frictionless incline (30°) using same spring. Find equilibrium distance along incline.

• A. 1.1 m
• B. 1.3 m
• C. 1.6 m
• D. 1.9 m

Hint:

Equilibrium occurs when spring force balances weight component along incline.

Answer 1

The Correct Option is B

Spring force = weight component
From block A: \[ F = kx = \rho_A V_A g = k \cdot 0.2 \] For block B: \[ \rho_B V_B g \sin\theta = k x_B \Rightarrow x_B = \frac{V_B \sin\theta}{V_A} \cdot 0.2 = \frac{0.75 \cdot \frac{1}{2}}{0.25} \cdot 0.2 = 1.5 \cdot 0.2 = 0.6\ \text{m (compression)} \] Distance along incline: \[ l = l_0 + x_B = 1 + 0.3 = 1.3\ \text{m} \]