---
title: "Two blocks of mass \\(m_1\\) and \\(m_2\\) are connected by an ideal string passing over a frictionless, massless pulley at the apex of a fixed double incline. The left incline is inclined at an angle \\(\\theta_1\\) above the horizontal, and the right incline is inclined at an angle \\(\\theta_2\\) above the horizontal. Both surfaces are frictionless, and \\(m_1 \\sin\\theta_1 > m_2 \\sin\\theta_2\\). Which of the following correctly describes the limiting behavior of the system’s acceleration \\(a\\) and the string tension \\(T\\) as \\(m_1 \\to \\infty\\) while \\(m_2\\), \\(\\theta_1\\), and \\(\\theta_2\\) are held fixed?"
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url: "https://nerd-notes.com/ubq/120565/"
date_modified: "2026-08-23T04:41:39+00:00"
---

# Two blocks of mass \(m_1\) and \(m_2\) are connected by an ideal string passing over a frictionless, massless pulley at the apex of a fixed double incline. The left incline is inclined at an angle \(\theta_1\) above the horizontal, and the right incline is inclined at an angle \(\theta_2\) above the horizontal. Both surfaces are frictionless, and \(m_1 \sin\theta_1 > m_2 \sin\theta_2\). Which of the following correctly describes the limiting behavior of the system’s acceleration \(a\) and the string tension \(T\) as \(m_1 \to \infty\) while \(m_2\), \(\theta_1\), and \(\theta_2\) are held fixed?

Two blocks of mass \(m_1\) and \(m_2\) are connected by an ideal string passing over a frictionless, massless pulley at the apex of a fixed double incline. The left incline is inclined at an angle \(\theta_1\) above the horizontal, and the right incline is inclined at an angle \(\theta_2\) above the horizontal. Both surfaces are frictionless, and \(m_1 \sin\theta_1 > m_2 \sin\theta_2\). Which of the following correctly describes the limiting behavior of the system's acceleration \(a\) and the string tension \(T\) as \(m_1 \to \infty\) while \(m_2\), \(\theta_1\), and \(\theta_2\) are held fixed?

![A triangular wedge rests on a horizontal base line. The left incline rises from the base at an angle labeled \theta_1, and the right incline descends to the base at an angle labeled \theta_2. At the top apex of the wedge, a small circular pulley is mounted. A rectangular block labeled m_1 sits on the left incline, and a rectangular block labeled m_2 sits on the right incline. A straight line representing a taut string extends from the top surface of block m_1 up along the left incline, wraps over the top of the pulley, and extends down along the right incline to the top surface of block m_2. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460098-vGnNWZ.jpg)

- **A.** \(a \to g \sin\theta_1\) and \(T \to \infty\), because the infinitely massive block exerts an unbounded pulling force on the string.
- **B.** \(a \to g \sin\theta_1\) and \(T \to m_2 g (\sin\theta_1 + \sin\theta_2)\), because block 1 accelerates as an unconstrained sliding mass while the tension must accelerate block 2 at \(g \sin\theta_1\) against gravity.
- **C.** \(a \to g\) and \(T \to m_2 g (\sin\theta_1 + \sin\theta_2)\), because any object of arbitrarily large mass approaches free-fall acceleration regardless of the incline angle.
- **D.** \(a \to g \sin\theta_1\) and \(T \to m_2 g \sin\theta_2\), because the tension in the string only needs to support the parallel component of gravity acting on block 2.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120565/*