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A body moves along a circular path of radius 5 m. The coefficient of friction between the surface of the path and the body is 0.5. The angular velocity in rad/s with which the body should move so that it does not leave the path is (g = 10 m/s2)
- a)4
- b)3
- c)2
- d)1
Correct answer is option 'D'. Can you explain this answer?
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A body moves along a circular path of radius 5 m. The coefficient of f...
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A body moves along a circular path of radius 5 m. The coefficient of f...
To solve this problem, we need to consider the forces acting on the body as it moves along the circular path.
1. Centripetal Force:
The centripetal force is responsible for keeping the body moving in a circular path. It is given by the equation Fc = m * (v^2 / r), where m is the mass of the body, v is the velocity, and r is the radius of the circular path.
2. Frictional Force:
The frictional force acts in the opposite direction to the motion of the body. It is given by the equation Ff = μ * N, where μ is the coefficient of friction and N is the normal force.
3. Normal Force:
The normal force is the force exerted by the surface of the path on the body. In this case, it is equal to the weight of the body, which is given by N = m * g, where g is the acceleration due to gravity.
The body will not leave the path if the centripetal force is greater than or equal to the frictional force.
Let's solve the problem step by step:
Step 1: Calculate the normal force
N = m * g
Step 2: Calculate the frictional force
Ff = μ * N
Step 3: Calculate the centripetal force
Fc = m * (v^2 / r)
Step 4: Equate the frictional force and the centripetal force
Ff = Fc
Step 5: Substitute the values and solve for v
μ * N = m * (v^2 / r)
Step 6: Substitute the value of N
μ * (m * g) = m * (v^2 / r)
Step 7: Simplify the equation
μ * g = v^2 / r
Step 8: Solve for v
v^2 = μ * g * r
Step 9: Take the square root of both sides
v = √(μ * g * r)
Step 10: Substitute the given values
v = √(0.5 * 10 * 5)
Step 11: Calculate the final answer
v = √(25)
v = 5 m/s
The angular velocity in rad/s is given by the formula ω = v / r, where v is the linear velocity and r is the radius of the circular path.
ω = 5 / 5
ω = 1 rad/s
Therefore, the correct answer is option D) 1 rad/s.
1. Centripetal Force:
The centripetal force is responsible for keeping the body moving in a circular path. It is given by the equation Fc = m * (v^2 / r), where m is the mass of the body, v is the velocity, and r is the radius of the circular path.
2. Frictional Force:
The frictional force acts in the opposite direction to the motion of the body. It is given by the equation Ff = μ * N, where μ is the coefficient of friction and N is the normal force.
3. Normal Force:
The normal force is the force exerted by the surface of the path on the body. In this case, it is equal to the weight of the body, which is given by N = m * g, where g is the acceleration due to gravity.
The body will not leave the path if the centripetal force is greater than or equal to the frictional force.
Let's solve the problem step by step:
Step 1: Calculate the normal force
N = m * g
Step 2: Calculate the frictional force
Ff = μ * N
Step 3: Calculate the centripetal force
Fc = m * (v^2 / r)
Step 4: Equate the frictional force and the centripetal force
Ff = Fc
Step 5: Substitute the values and solve for v
μ * N = m * (v^2 / r)
Step 6: Substitute the value of N
μ * (m * g) = m * (v^2 / r)
Step 7: Simplify the equation
μ * g = v^2 / r
Step 8: Solve for v
v^2 = μ * g * r
Step 9: Take the square root of both sides
v = √(μ * g * r)
Step 10: Substitute the given values
v = √(0.5 * 10 * 5)
Step 11: Calculate the final answer
v = √(25)
v = 5 m/s
The angular velocity in rad/s is given by the formula ω = v / r, where v is the linear velocity and r is the radius of the circular path.
ω = 5 / 5
ω = 1 rad/s
Therefore, the correct answer is option D) 1 rad/s.
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A body moves along a circular path of radius 5 m. The coefficient of friction between the surface of the path and the body is 0.5. The angular velocity in rad/s with which the body should move so that it does not leave the path is (g = 10 m/s2) a)4 b)3 c)2 d)1 Correct answer is option 'D'. Can you explain this answer? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A body moves along a circular path of radius 5 m. The coefficient of friction between the surface of the path and the body is 0.5. The angular velocity in rad/s with which the body should move so that it does not leave the path is (g = 10 m/s2) a)4 b)3 c)2 d)1 Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body moves along a circular path of radius 5 m. The coefficient of friction between the surface of the path and the body is 0.5. The angular velocity in rad/s with which the body should move so that it does not leave the path is (g = 10 m/s2) a)4 b)3 c)2 d)1 Correct answer is option 'D'. Can you explain this answer?.
A body moves along a circular path of radius 5 m. The coefficient of friction between the surface of the path and the body is 0.5. The angular velocity in rad/s with which the body should move so that it does not leave the path is (g = 10 m/s2) a)4 b)3 c)2 d)1 Correct answer is option 'D'. Can you explain this answer? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A body moves along a circular path of radius 5 m. The coefficient of friction between the surface of the path and the body is 0.5. The angular velocity in rad/s with which the body should move so that it does not leave the path is (g = 10 m/s2) a)4 b)3 c)2 d)1 Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body moves along a circular path of radius 5 m. The coefficient of friction between the surface of the path and the body is 0.5. The angular velocity in rad/s with which the body should move so that it does not leave the path is (g = 10 m/s2) a)4 b)3 c)2 d)1 Correct answer is option 'D'. Can you explain this answer?.
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