Two masses m1 and m2 are attached to a string which passes...

Two masses $m_{1}$ and $m_{2}$ are attached to a string which passes over a frictionless smooth pulley. When $m_{1}=10 \mathrm{~kg}, m_{2}=6 \mathrm{~kg}$, the acceleration of masses is $\quad$ (a) $20 \mathrm{~m} / \mathrm{s}^{2}$ (b) $5 \mathrm{~m} / \mathrm{s}^{2}$ (c) $2.5 \mathrm{~m} / \mathrm{s}^{2}$ (d) $10 \mathrm{~m} / \mathrm{s}^{2}$

Two masses $m_{1}$ and $m_{2}$ are attached to a string which passes over a frictionless smooth pulley. When $m_{1}=10 \mathrm{~kg}, m_{2}=6 \mathrm{~kg}$, the acceleration of masses is $\quad$
(a) $20 \mathrm{~m} / \mathrm{s}^{2}$
(b) $5 \mathrm{~m} / \mathrm{s}^{2}$
(c) $2.5 \mathrm{~m} / \mathrm{s}^{2}$
(d) $10 \mathrm{~m} / \mathrm{s}^{2}$

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Key Concepts

Newton's Second Law

Newton's Second Law states that the net force acting on an object is equal to the product of its mass and its acceleration (F=ma). This principle is fundamental in analyzing the motion in any system involving forces, including systems with connected masses.

Atwood's Machine

An Atwood's machine is a simple mechanical system consisting of two masses connected by a string over a pulley. It serves as a classic example to study the dynamics of motion under the influence of gravitational force and demonstrates how differences in mass lead to linear acceleration.

Frictionless Pulley

A frictionless pulley assumes that there is no friction in the pulley mechanism, which means the tension remains uniform throughout the string. This assumption simplifies the mathematical analysis of the forces acting on the masses, allowing for a direct application of Newton's laws.

Gravitational Force

Gravitational force is the attractive force exerted by the Earth on masses. In dynamics problems involving connected objects, the difference in gravitational force on unequal masses results in a net force that causes acceleration, a key aspect in analyzing systems like the Atwood's machine.

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