Two blocks are connected by a string as shown in the...

Two blocks are connected by a string as shown in the diagram. The upper block is hung by another string. A force applied on the upper string produces an acceleration of $2 \mathrm{~m} / \mathrm{s}^{2}$ in the upward direction in both the blocks. If $T$ and $T^{\prime}$ be the tensions in the two parts of the string, then $\left(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)$ (a) $T=70.8 \mathrm{~N}$ and $T^{\prime}=47,2 \mathrm{~N}$ (b) $T=58.8 \mathrm{~N}$ and $T^{*}=47.2 \mathrm{~N}$ (c) $T=70.8 \mathrm{~N}$ and $T^{\prime}=58.8 \mathrm{~N}$ (d) $T=70.8 \mathrm{~N}$ and $T^{\prime}=0$

Two blocks are connected by a string as shown in the diagram. The upper block is hung by another string. A force applied on the upper string produces an acceleration of $2 \mathrm{~m} / \mathrm{s}^{2}$ in the upward direction in both the blocks. If $T$ and $T^{\prime}$ be the tensions in the two parts of the string, then $\left(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)$
(a) $T=70.8 \mathrm{~N}$ and $T^{\prime}=47,2 \mathrm{~N}$
(b) $T=58.8 \mathrm{~N}$ and $T^{*}=47.2 \mathrm{~N}$
(c) $T=70.8 \mathrm{~N}$ and $T^{\prime}=58.8 \mathrm{~N}$
(d) $T=70.8 \mathrm{~N}$ and $T^{\prime}=0$

Key Concepts

Acceleration in a Gravitational Field

In problems where objects accelerate in a gravitational field, it is important to account for the weight of each object (mass multiplied by the gravitational acceleration). The net force acting on the objects is determined by both the applied forces and the gravitational force, which influences the tension in the strings and the overall motion of the system.

Connected System Dynamics

When bodies are connected by strings or rods, their motions are constrained to be related. This means that the acceleration of one body is directly related to the acceleration of the connected bodies. Establishing these relationships is vital when applying Newton's Second Law to each part of the system to derive a set of simultaneous equations that can be solved for the unknowns.

Newton's Second Law

This concept states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = m·a). It is fundamental in analyzing the motion of any object, including systems with multiple connected bodies. In problems involving forces and accelerations, applying this law to each component helps to set up the equations needed to solve for unknown forces such as tension.

Free-Body Diagrams

A free-body diagram is a graphical representation used to visualize the forces acting on a single object. In dynamics problems, each object is isolated and all forces, such as gravitational force, tension, and applied forces, are depicted as vectors. These diagrams are essential in correctly identifying and setting up the force equations according to Newton's laws.

Tension in Strings

Tension refers to the pulling force transmitted along a string, rope, or cable when forces are applied at its ends. In ideal situations, strings are considered massless and inextensible, which allows the same tension to be used throughout a continuous segment of the string. Analyzing the tensions in various parts of a connected system is critical for solving for unknown forces and accelerations.

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