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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.
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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?.
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