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A small body f mass m can slide without friction along a trough which is bent in the form of semi circle of radius R. At what height h will the body be at rest w.r.t. the trough if the trough rotates with uniform angular velocity 'w' about a vertical axis is?
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Analysis:
To solve this problem, we can consider the forces acting on the body at rest in the trough. There are two forces to consider: the gravitational force and the centrifugal force.
Gravitational Force:
The gravitational force acting on the body is given by Fg = mg, where m is the mass of the body and g is the acceleration due to gravity.
Centrifugal Force:
The centrifugal force is the apparent outward force experienced by an object moving in a circular path. It can be calculated using the equation Fc = mw^2R, where m is the mass of the body, w is the angular velocity of the trough, and R is the radius of the trough.
Equilibrium Condition:
Since the body is at rest, the net force acting on it must be zero. Therefore, the gravitational force and the centrifugal force must balance each other.
Equating Forces:
We can equate the gravitational force and the centrifugal force to find the height at which the body will be at rest.
mg = mw^2R
Simplifying and Solving for height:
Dividing both sides of the equation by m, we get:
g = w^2R
Solving for R, we get:
R = g/w^2
The height h can be obtained by subtracting R from the radius of the trough:
h = R - R*cos(theta)
Final Answer:
The height at which the body will be at rest with respect to the trough is given by:
h = g/w^2 - (g/w^2)*cos(theta)
where g is the acceleration due to gravity, w is the angular velocity of the trough, and theta is the angle between the vertical axis and the line connecting the center of the trough to the body.
To solve this problem, we can consider the forces acting on the body at rest in the trough. There are two forces to consider: the gravitational force and the centrifugal force.
Gravitational Force:
The gravitational force acting on the body is given by Fg = mg, where m is the mass of the body and g is the acceleration due to gravity.
Centrifugal Force:
The centrifugal force is the apparent outward force experienced by an object moving in a circular path. It can be calculated using the equation Fc = mw^2R, where m is the mass of the body, w is the angular velocity of the trough, and R is the radius of the trough.
Equilibrium Condition:
Since the body is at rest, the net force acting on it must be zero. Therefore, the gravitational force and the centrifugal force must balance each other.
Equating Forces:
We can equate the gravitational force and the centrifugal force to find the height at which the body will be at rest.
mg = mw^2R
Simplifying and Solving for height:
Dividing both sides of the equation by m, we get:
g = w^2R
Solving for R, we get:
R = g/w^2
The height h can be obtained by subtracting R from the radius of the trough:
h = R - R*cos(theta)
Final Answer:
The height at which the body will be at rest with respect to the trough is given by:
h = g/w^2 - (g/w^2)*cos(theta)
where g is the acceleration due to gravity, w is the angular velocity of the trough, and theta is the angle between the vertical axis and the line connecting the center of the trough to the body.
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A small body f mass m can slide without friction along a trough which is bent in the form of semi circle of radius R. At what height h will the body be at rest w.r.t. the trough if the trough rotates with uniform angular velocity 'w' about a vertical axis is?
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A small body f mass m can slide without friction along a trough which is bent in the form of semi circle of radius R. At what height h will the body be at rest w.r.t. the trough if the trough rotates with uniform angular velocity 'w' about a vertical axis is? 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 body f mass m can slide without friction along a trough which is bent in the form of semi circle of radius R. At what height h will the body be at rest w.r.t. the trough if the trough rotates with uniform angular velocity 'w' about a vertical axis is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A small body f mass m can slide without friction along a trough which is bent in the form of semi circle of radius R. At what height h will the body be at rest w.r.t. the trough if the trough rotates with uniform angular velocity 'w' about a vertical axis is?.
A small body f mass m can slide without friction along a trough which is bent in the form of semi circle of radius R. At what height h will the body be at rest w.r.t. the trough if the trough rotates with uniform angular velocity 'w' about a vertical axis is? 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 body f mass m can slide without friction along a trough which is bent in the form of semi circle of radius R. At what height h will the body be at rest w.r.t. the trough if the trough rotates with uniform angular velocity 'w' about a vertical axis is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A small body f mass m can slide without friction along a trough which is bent in the form of semi circle of radius R. At what height h will the body be at rest w.r.t. the trough if the trough rotates with uniform angular velocity 'w' about a vertical axis is?.
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