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a 4m long ladder weighing 25 kg rests with its upper end against a smooth wall and lower end on rough ground. what should be min. coeff. of friction between the ground and the ladder for it to be inclined at 60degree with the horizontal without sleeping?1. 0.192. 0.293. 0.394. 0.49
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a 4m long ladder weighing 25 kg rests with its upper end against a smo...
The Minimum Coefficient of Friction for a Ladder
In order to determine the minimum coefficient of friction between the ground and the ladder, we need to analyze the forces acting on the ladder.
Forces Acting on the Ladder
There are three main forces acting on the ladder:
- Weight of the ladder: The weight of the ladder is acting vertically downwards and can be calculated using the formula W = mg, where m is the mass of the ladder and g is the acceleration due to gravity.
- Normal force: The normal force is the force exerted by the ground on the ladder and acts perpendicular to the ground. It cancels out the vertical component of the weight of the ladder.
- Frictional force: The frictional force acts parallel to the ground and opposes the motion of the ladder. It can be calculated using the formula F = μN, where μ is the coefficient of friction and N is the normal force.
Analysis of the Forces
Considering the ladder is inclined at 60 degrees with the horizontal, we can resolve the weight of the ladder into two components:
- Vertical component: This component is equal to W * cos(60).
- Horizontal component: This component is equal to W * sin(60).
The normal force will cancel out the vertical component of the weight, leaving only the horizontal component to be balanced by the frictional force.
Calculating the Minimum Coefficient of Friction
In order for the ladder not to slip, the frictional force must be equal to or greater than the horizontal component of the weight of the ladder. Therefore, we can set up the following inequality:
- μN ≥ W * sin(60)
Since N = W * cos(60), we can substitute it into the inequality:
- μ * (W * cos(60)) ≥ W * sin(60)
Canceling out the weight on both sides:
- μ * cos(60) ≥ sin(60)
Using the values of cos(60) = 0.5 and sin(60) = √3/2:
- μ * 0.5 ≥ √3/2
Simplifying further:
- μ ≥ √3
Therefore, the minimum coefficient of friction between the ground and the ladder should be greater than or equal to √3 or approximately 1.732. None of the given options (0.19, 0.29, 0.39, or 0.49) satisfy this condition. Hence, none of the provided options are correct.
Community Answer
a 4m long ladder weighing 25 kg rests with its upper end against a smo...
0.2941
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a 4m long ladder weighing 25 kg rests with its upper end against a smooth wall and lower end on rough ground. what should be min. coeff. of friction between the ground and the ladder for it to be inclined at 60degree with the horizontal without sleeping?1. 0.192. 0.293. 0.394. 0.49
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a 4m long ladder weighing 25 kg rests with its upper end against a smooth wall and lower end on rough ground. what should be min. coeff. of friction between the ground and the ladder for it to be inclined at 60degree with the horizontal without sleeping?1. 0.192. 0.293. 0.394. 0.49 for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about a 4m long ladder weighing 25 kg rests with its upper end against a smooth wall and lower end on rough ground. what should be min. coeff. of friction between the ground and the ladder for it to be inclined at 60degree with the horizontal without sleeping?1. 0.192. 0.293. 0.394. 0.49 covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for a 4m long ladder weighing 25 kg rests with its upper end against a smooth wall and lower end on rough ground. what should be min. coeff. of friction between the ground and the ladder for it to be inclined at 60degree with the horizontal without sleeping?1. 0.192. 0.293. 0.394. 0.49.
a 4m long ladder weighing 25 kg rests with its upper end against a smooth wall and lower end on rough ground. what should be min. coeff. of friction between the ground and the ladder for it to be inclined at 60degree with the horizontal without sleeping?1. 0.192. 0.293. 0.394. 0.49 for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about a 4m long ladder weighing 25 kg rests with its upper end against a smooth wall and lower end on rough ground. what should be min. coeff. of friction between the ground and the ladder for it to be inclined at 60degree with the horizontal without sleeping?1. 0.192. 0.293. 0.394. 0.49 covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for a 4m long ladder weighing 25 kg rests with its upper end against a smooth wall and lower end on rough ground. what should be min. coeff. of friction between the ground and the ladder for it to be inclined at 60degree with the horizontal without sleeping?1. 0.192. 0.293. 0.394. 0.49.
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