Two blocks of mass m=5 kg and M=10 kg are connected by a light string passing over a pulley B

step 1 So let's solve this question for the first part t equals to 75 4 that equals to 125 Newton s t i

Two blocks of mass m=5 kg and M=10 kg are connected by a...

Two blocks of mass $m=5 \mathrm{~kg}$ and $M=10 \mathrm{~kg}$ are connected by a light string passing over a pulley $B$ as shown. $\Lambda$ nother light string connects the centre of pulley $B$ to the floor and passes over another pulley $A$ as shown. $\Lambda$ n upward force $F$ is applied at the centre of pulley $A$. Both the pulleys are massless. Find the acceleration of block $m$ and $M$, if $F$ is: (a) $500 \mathrm{~N}$ (b) $300 \mathrm{~N}$ (c) $100 \mathrm{~N}\left(\mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$ Solution string string $T_{0} \quad T_{0}$ T $T$ (a) $T^{\prime}=F / 4=125 \mathrm{~N}$ $\Lambda \mathrm{s} T>m y$ and $\mathrm{Mg}$, both the blocks will accelerate upwards. \Lambdacceleration of $m, a_{1}=\frac{T-m g}{m}=\frac{125-50}{5}=15 \mathrm{~m} / \mathrm{s}^{2}$ \Lambdacceleration of $M, a_{2}=\frac{T-M g}{M}=\frac{125-100}{10}=2.5 \mathrm{~m} / \mathrm{s}^{2}$ (b) $7^{\prime}=F / 4=75 \mathrm{~N}$ \Lambdas $T<M g$ and $T>m g, M$ will remain stationary on the floor, where as $m$ will move. Accclcration of $i n, a_{1}-\frac{T-m g}{m}-\frac{75-50}{5}-5 \mathrm{~m} / \mathrm{s}^{2}$ (c) $T=F / 4=25 \mathrm{~N}$ $\begin{array}{ll}\text { weights of blocks are } & m g=50 \mathrm{~N}\end{array} \quad M g=100 \mathrm{~N}$ \Lambdas $7<m g$ and $M g$ both, the blocks will remain stationary on the floor.

Two blocks of mass $m=5 \mathrm{~kg}$ and $M=10 \mathrm{~kg}$ are connected by a light string passing over a pulley $B$ as shown. $\Lambda$ nother light string connects the centre of pulley $B$ to the floor and passes over another pulley $A$ as shown. $\Lambda$ n upward force $F$ is applied at the centre of pulley $A$. Both the pulleys are massless. Find the acceleration of block $m$ and $M$, if $F$ is:
(a) $500 \mathrm{~N}$
(b) $300 \mathrm{~N}$
(c) $100 \mathrm{~N}\left(\mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
Solution string string
$T_{0} \quad T_{0}$
T $T$
(a) $T^{\prime}=F / 4=125 \mathrm{~N}$
$\Lambda \mathrm{s} T>m y$ and $\mathrm{Mg}$, both the blocks will accelerate upwards. \Lambdacceleration of $m, a_{1}=\frac{T-m g}{m}=\frac{125-50}{5}=15 \mathrm{~m} / \mathrm{s}^{2}$
\Lambdacceleration of $M, a_{2}=\frac{T-M g}{M}=\frac{125-100}{10}=2.5 \mathrm{~m} / \mathrm{s}^{2}$
(b) $7^{\prime}=F / 4=75 \mathrm{~N}$
\Lambdas $T<M g$ and $T>m g, M$ will remain stationary on the floor, where as $m$ will move. Accclcration of $i n, a_{1}-\frac{T-m g}{m}-\frac{75-50}{5}-5 \mathrm{~m} / \mathrm{s}^{2}$
(c) $T=F / 4=25 \mathrm{~N}$
$\begin{array}{ll}\text { weights of blocks are } & m g=50 \mathrm{~N}\end{array} \quad M g=100 \mathrm{~N}$
\Lambdas $7<m g$ and $M g$ both, the blocks will remain stationary on the floor.

Key Concepts

Newton's Second Law

This concept governs the relation between the net force acting on an object and its resultant acceleration (F = ma). In problems involving blocks and pulleys, it forms the basis for setting up equations of motion for each mass, accounting for gravitational forces, tension, and applied forces.

Tension in Massless Strings

In systems with massless strings and pulleys, the tension is transmitted uniformly along the string (when frictionless and massless). This assumption simplifies the analysis by allowing one to equate forces in different segments of the string, which is crucial for solving the motion dynamics of connected masses.

Pulley Systems and Force Distribution

Pulley systems alter the effective magnitude and direction of forces. In a compound pulley system, the applied force is distributed among multiple segments of the string, reducing the force acting on each mass. Understanding this distribution is essential to correctly determine the tensions and subsequent accelerations in the system.

Free-Body Diagrams

Drawing free-body diagrams is a key technique for visualizing all the forces acting on each component of the system, including weights, tensions, and applied forces. This method is indispensable for setting up the correct equations to analyze the motion of interconnected bodies.

Conditions for Motion and Equilibrium

Determining whether a mass will accelerate, remain at rest, or move with a certain acceleration involves comparing forces such as gravitational force and tension. Establishing these conditions allows one to understand thresholds of applied force that change the motion state of the system.

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