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 $F$ 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 $\quad$ (a) $T=70.8 \mathrm{~N}$ and $T^{\prime}=47.2 \mathrm{~N}$ (b) $T=58.8 N$ and $T^{\prime}=47.2 N$ (c) $T=70.8 N$ and $T^{\prime}=58.8 N$ (d) $T=70.8 N$ 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 $F$ 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 $\quad$
(a) $T=70.8 \mathrm{~N}$ and $T^{\prime}=47.2 \mathrm{~N}$
(b) $T=58.8 N$ and $T^{\prime}=47.2 N$
(c) $T=70.8 N$ and $T^{\prime}=58.8 N$
(d) $T=70.8 N$ and $T^{\prime}=0$

Key Concepts

Newton's Second Law

This law states that the net force acting on an object is equal to the mass of that object multiplied by its acceleration (F = ma). It is fundamental in analyzing the motion of objects under the influence of various forces, and it serves as the basis for setting up equations that describe the dynamics of systems, such as connected blocks under tension.

Free Body Diagrams

A free body diagram is a graphical representation used to visualize the forces acting on a single object. By isolating each block or component and drawing all the forces including gravity, tension, friction and applied forces, one can apply Newton's laws more clearly and set up the equations needed to solve for unknown quantities in the problem.

Tension in Strings

Tension is the pulling force transmitted through a string, rope, or cable when forces are applied at its ends. In problems involving multiple connected objects, the tension can vary along different segments of the string, especially when different forces or accelerations are acting on the system, making it a key concept to analyze.

Dynamics of Connected Bodies

This concept involves studying how multiple objects linked by strings or other connectors move together when forces are applied. It requires understanding the individual forces acting on each object and recognizing that their accelerations are related. This approach often leads to a set of simultaneous equations that must be solved to determine quantities like tension and acceleration.

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