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Starting from rest, a body slides down a 45∘ inclined plane in twice the time it takes to slide the same distance in the absence of friction. What is the coefficient of friction between the body and the inclined plane?
- a)√3/2
- b)3/4
- c)1/2
- d)1/4
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Starting from rest, a body slides down a 45 inclined plane in twice th...
For a frictionless surface,
In the presence of friction,
Dividing eq. (2) by eq. (1), we get
In the presence of friction,
Dividing eq. (2) by eq. (1), we get
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Starting from rest, a body slides down a 45 inclined plane in twice th...
Understanding the Problem
The problem involves a body sliding down a 45-degree inclined plane with friction. Given that the time taken to slide down is doubled compared to when there is no friction, we need to find the coefficient of friction.
Key Concepts
- Inclined Plane Dynamics: When sliding down a frictionless incline, the acceleration is due to gravity's component along the incline.
- Friction's Role: Friction reduces the body's acceleration, affecting the time taken to slide down.
Equations of Motion
1. Without Friction:
- Acceleration (a) = g * sin(θ)
- For θ = 45 degrees, a = g / √2.
- Time (t_frictionless) = √(2d/a) = √(2d/(g/√2)) = √(4d/ g).
2. With Friction:
- Effective acceleration (a_effective) = g * sin(θ) - f/m (where f is friction).
- f = μ * N = μ * mg * cos(θ), leading to a_effective = g / √2 - μg / 2.
- Time (t_friction) = √(2d/a_effective) = √(2d/(g/√2 - μg/2)).
Setting Up the Equation
Given that t_friction = 2 * t_frictionless, we can establish:
√(2d/(g/√2 - μg/2)) = 2 * √(4d/g).
Squaring both sides and simplifying gives:
2d/(g/√2 - μg/2) = 16d/g.
After canceling d and rearranging, we find:
g/√2 - μg/2 = g/8.
Finding the Coefficient of Friction
Solving the equation leads to:
μ = 3/4.
Thus, the coefficient of friction between the body and the inclined plane is 3/4, confirming option B as the correct answer.
The problem involves a body sliding down a 45-degree inclined plane with friction. Given that the time taken to slide down is doubled compared to when there is no friction, we need to find the coefficient of friction.
Key Concepts
- Inclined Plane Dynamics: When sliding down a frictionless incline, the acceleration is due to gravity's component along the incline.
- Friction's Role: Friction reduces the body's acceleration, affecting the time taken to slide down.
Equations of Motion
1. Without Friction:
- Acceleration (a) = g * sin(θ)
- For θ = 45 degrees, a = g / √2.
- Time (t_frictionless) = √(2d/a) = √(2d/(g/√2)) = √(4d/ g).
2. With Friction:
- Effective acceleration (a_effective) = g * sin(θ) - f/m (where f is friction).
- f = μ * N = μ * mg * cos(θ), leading to a_effective = g / √2 - μg / 2.
- Time (t_friction) = √(2d/a_effective) = √(2d/(g/√2 - μg/2)).
Setting Up the Equation
Given that t_friction = 2 * t_frictionless, we can establish:
√(2d/(g/√2 - μg/2)) = 2 * √(4d/g).
Squaring both sides and simplifying gives:
2d/(g/√2 - μg/2) = 16d/g.
After canceling d and rearranging, we find:
g/√2 - μg/2 = g/8.
Finding the Coefficient of Friction
Solving the equation leads to:
μ = 3/4.
Thus, the coefficient of friction between the body and the inclined plane is 3/4, confirming option B as the correct answer.
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Starting from rest, a body slides down a 45 inclined plane in twice the time it takes to slide the same distance in the absence of friction. What is the coefficient of friction between the body and the inclined plane?a)√3/2b)3/4c)1/2d)1/4Correct answer is option 'B'. Can you explain this answer? for NEET 2026 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Starting from rest, a body slides down a 45 inclined plane in twice the time it takes to slide the same distance in the absence of friction. What is the coefficient of friction between the body and the inclined plane?a)√3/2b)3/4c)1/2d)1/4Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Starting from rest, a body slides down a 45 inclined plane in twice the time it takes to slide the same distance in the absence of friction. What is the coefficient of friction between the body and the inclined plane?a)√3/2b)3/4c)1/2d)1/4Correct answer is option 'B'. Can you explain this answer?.
Starting from rest, a body slides down a 45 inclined plane in twice the time it takes to slide the same distance in the absence of friction. What is the coefficient of friction between the body and the inclined plane?a)√3/2b)3/4c)1/2d)1/4Correct answer is option 'B'. Can you explain this answer? for NEET 2026 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Starting from rest, a body slides down a 45 inclined plane in twice the time it takes to slide the same distance in the absence of friction. What is the coefficient of friction between the body and the inclined plane?a)√3/2b)3/4c)1/2d)1/4Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Starting from rest, a body slides down a 45 inclined plane in twice the time it takes to slide the same distance in the absence of friction. What is the coefficient of friction between the body and the inclined plane?a)√3/2b)3/4c)1/2d)1/4Correct answer is option 'B'. Can you explain this answer?.
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