Three blocks of masses m1, m2 and m3 are connected by mass...

Three blocks of masses $m_{1}, m_{2}$ and $m_{3}$ are connected by mass less strings as shown in figure, on a frictionless table. They are Pulled with a force $\mathrm{T}_{3}=40 \mathrm{~N}$. If $\mathrm{m}_{1}=10 \mathrm{~kg}$, $\mathrm{m}_{2}=6 \mathrm{~kg}$ and $\mathrm{m}_{3}=4 \mathrm{~kg}$ the tension $\mathrm{T}_{2}$ will be $=$ $\mathrm{N}$ (A) 20 (B) 40 (C) 10 (D) 32

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 acceleration (F = ma). This principle is fundamental for analyzing the dynamics of systems, including multiple bodies in motion, and is used to determine acceleration when forces and masses are known.

Tension in Massless Strings

In mechanics, when strings are considered massless, the tension is assumed to be uniform throughout each segment of the string. This simplification allows for easier analysis of connected objects, as the force transmitted along the string does not vary due to the string’s mass, and it provides a direct relationship between the forces acting on different masses.

Systems of Connected Masses

Systems of connected masses involve multiple objects linked by connectors such as strings or rods. These systems are analyzed by considering the motion and interactions of each mass together as well as individually, often using the common acceleration of the system and balancing the forces at the connection points.

Free Body Diagram Analysis

Free body diagrams are graphical representations used to visualize the forces acting on each object in a system. By isolating each mass and identifying all the forces, such diagrams help in setting up the equations based on Newton's laws, simplifying the process of solving for unknown quantities like tension or acceleration.

Please give Ace some feedback