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A small pulley of radius 20 cm and moment of inertia 0.32 kgm2 (square) is used to hang a block of mass 2 kg with the help of a massless string . If the block is released , for no slipping condition , find the acceleration of the block (a) 1 m/ second square (b) 2 m / second square (c) 3 m / second square (d) 5 m / second square?
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A small pulley of radius 20 cm and moment of inertia 0.32 kgm2 (square...
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A small pulley of radius 20 cm and moment of inertia 0.32 kgm2 (square...
< b="" />Pulley and Block System
The given problem involves a small pulley and a block connected by a massless string. The pulley has a radius of 20 cm and a moment of inertia of 0.32 kgm^2. The block has a mass of 2 kg.
< b="" />Finding the Acceleration
To find the acceleration of the block, we need to consider the forces acting on it. Since the string is massless, the tension in the string will be the same at all points.
< b="" />Forces Acting on the Block
- Tension force from the string
- Weight force due to gravity
Since the block is released, it is free to move under the influence of these forces. The acceleration of the block will depend on the net force acting on it.
< b="" />Torque on the Pulley
The torque on the pulley will cause it to rotate. We can calculate the torque using the formula:
Torque = moment of inertia * angular acceleration
< b="" />Angular Acceleration
The angular acceleration of the pulley can be calculated using the formula:
Angular acceleration = acceleration / radius
< b="" />Net Force on the Block
The net force on the block is given by the equation:
Net force = mass * acceleration
< b="" />Equating Torque and Net Force
Since the string is massless, the tension force on both sides of the pulley will be the same. We can equate the torque on the pulley to the net force on the block:
Torque = Net force * radius
< b="" />Solving the Equation
Substituting the values into the equation, we have:
0.32 * angular acceleration = 2 * acceleration * 0.2
Simplifying the equation, we get:
angular acceleration = 10 * acceleration
< b="" />Acceleration of the Block
Since the angular acceleration is related to the linear acceleration, we can substitute the equation for angular acceleration into the equation for net force:
0.32 * 10 * acceleration = 2 * acceleration
Simplifying the equation, we find:
3.2 * acceleration = 2 * acceleration
< b="" />Final Answer
From the equation above, we can see that the acceleration cancels out. Therefore, the acceleration of the block is independent of the mass and moment of inertia of the pulley. Thus, the acceleration of the block is < b="" />2 m/s^2.
So, the correct option is < b="" />(b) 2 m/s^2.
The given problem involves a small pulley and a block connected by a massless string. The pulley has a radius of 20 cm and a moment of inertia of 0.32 kgm^2. The block has a mass of 2 kg.
< b="" />Finding the Acceleration
To find the acceleration of the block, we need to consider the forces acting on it. Since the string is massless, the tension in the string will be the same at all points.
< b="" />Forces Acting on the Block
- Tension force from the string
- Weight force due to gravity
Since the block is released, it is free to move under the influence of these forces. The acceleration of the block will depend on the net force acting on it.
< b="" />Torque on the Pulley
The torque on the pulley will cause it to rotate. We can calculate the torque using the formula:
Torque = moment of inertia * angular acceleration
< b="" />Angular Acceleration
The angular acceleration of the pulley can be calculated using the formula:
Angular acceleration = acceleration / radius
< b="" />Net Force on the Block
The net force on the block is given by the equation:
Net force = mass * acceleration
< b="" />Equating Torque and Net Force
Since the string is massless, the tension force on both sides of the pulley will be the same. We can equate the torque on the pulley to the net force on the block:
Torque = Net force * radius
< b="" />Solving the Equation
Substituting the values into the equation, we have:
0.32 * angular acceleration = 2 * acceleration * 0.2
Simplifying the equation, we get:
angular acceleration = 10 * acceleration
< b="" />Acceleration of the Block
Since the angular acceleration is related to the linear acceleration, we can substitute the equation for angular acceleration into the equation for net force:
0.32 * 10 * acceleration = 2 * acceleration
Simplifying the equation, we find:
3.2 * acceleration = 2 * acceleration
< b="" />Final Answer
From the equation above, we can see that the acceleration cancels out. Therefore, the acceleration of the block is independent of the mass and moment of inertia of the pulley. Thus, the acceleration of the block is < b="" />2 m/s^2.
So, the correct option is < b="" />(b) 2 m/s^2.
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A small pulley of radius 20 cm and moment of inertia 0.32 kgm2 (square) is used to hang a block of mass 2 kg with the help of a massless string . If the block is released , for no slipping condition , find the acceleration of the block (a) 1 m/ second square (b) 2 m / second square (c) 3 m / second square (d) 5 m / second square?
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A small pulley of radius 20 cm and moment of inertia 0.32 kgm2 (square) is used to hang a block of mass 2 kg with the help of a massless string . If the block is released , for no slipping condition , find the acceleration of the block (a) 1 m/ second square (b) 2 m / second square (c) 3 m / second square (d) 5 m / second square? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A small pulley of radius 20 cm and moment of inertia 0.32 kgm2 (square) is used to hang a block of mass 2 kg with the help of a massless string . If the block is released , for no slipping condition , find the acceleration of the block (a) 1 m/ second square (b) 2 m / second square (c) 3 m / second square (d) 5 m / second square? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A small pulley of radius 20 cm and moment of inertia 0.32 kgm2 (square) is used to hang a block of mass 2 kg with the help of a massless string . If the block is released , for no slipping condition , find the acceleration of the block (a) 1 m/ second square (b) 2 m / second square (c) 3 m / second square (d) 5 m / second square?.
A small pulley of radius 20 cm and moment of inertia 0.32 kgm2 (square) is used to hang a block of mass 2 kg with the help of a massless string . If the block is released , for no slipping condition , find the acceleration of the block (a) 1 m/ second square (b) 2 m / second square (c) 3 m / second square (d) 5 m / second square? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A small pulley of radius 20 cm and moment of inertia 0.32 kgm2 (square) is used to hang a block of mass 2 kg with the help of a massless string . If the block is released , for no slipping condition , find the acceleration of the block (a) 1 m/ second square (b) 2 m / second square (c) 3 m / second square (d) 5 m / second square? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A small pulley of radius 20 cm and moment of inertia 0.32 kgm2 (square) is used to hang a block of mass 2 kg with the help of a massless string . If the block is released , for no slipping condition , find the acceleration of the block (a) 1 m/ second square (b) 2 m / second square (c) 3 m / second square (d) 5 m / second square?.
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