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A block takes twice as much time to slide down a 45o rough inclined plane as it takes to slide down a similar smooth plane. The coefficient of friction is
- a)3/4
- b)3/2
- c)1/4
- d)1/3
Correct answer is option 'A'. Can you explain this answer?
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A block takes twice as much time to slide down a 45o rough inclined pl...
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A block takes twice as much time to slide down a 45o rough inclined pl...
Given:
Angle of inclined plane = 45o
Coefficient of friction = ?
Let the height of the inclined plane be ‘h’ and distance travelled be ‘d’.
Concept:
When a body slides down an inclined plane, it experiences two types of forces:
1. Gravitational force (mg) acting vertically downwards.
2. Normal force (N) acting perpendicular to the plane and counteracting the gravitational force.
When the plane is rough, there is also a force of friction (f) acting opposite to the direction of motion of the block. The frictional force is given by f = µN, where µ is the coefficient of friction.
When the plane is smooth, there is no frictional force acting on the block. Hence, the block slides down the plane with a greater acceleration than in the case of a rough plane.
Calculation:
Let the time taken to slide down the smooth plane be ‘t’.
Acceleration of the block on the smooth plane, a = g sin 45o
Distance travelled, d = 1/2 a t^2
Time taken, t = √(2d/a)
Let the time taken to slide down the rough plane be ‘2t’.
Acceleration of the block on the rough plane, a' = g sin 45o - µg cos 45o
Distance travelled, d = 1/2 a' (2t)^2 = 2a' t^2
Time taken, 2t = √(2d/a')
As per the given condition, 2t = 2t x (3/2)
=> √(2d/a') = (3/2) √(2d/a)
=> a'/a = 9/4
=> g sin 45o - µg cos 45o = (9/4) g sin 45o
=> µ = (3/4)
Therefore, the coefficient of friction is 3/4. Answer: (a).
Angle of inclined plane = 45o
Coefficient of friction = ?
Let the height of the inclined plane be ‘h’ and distance travelled be ‘d’.
Concept:
When a body slides down an inclined plane, it experiences two types of forces:
1. Gravitational force (mg) acting vertically downwards.
2. Normal force (N) acting perpendicular to the plane and counteracting the gravitational force.
When the plane is rough, there is also a force of friction (f) acting opposite to the direction of motion of the block. The frictional force is given by f = µN, where µ is the coefficient of friction.
When the plane is smooth, there is no frictional force acting on the block. Hence, the block slides down the plane with a greater acceleration than in the case of a rough plane.
Calculation:
Let the time taken to slide down the smooth plane be ‘t’.
Acceleration of the block on the smooth plane, a = g sin 45o
Distance travelled, d = 1/2 a t^2
Time taken, t = √(2d/a)
Let the time taken to slide down the rough plane be ‘2t’.
Acceleration of the block on the rough plane, a' = g sin 45o - µg cos 45o
Distance travelled, d = 1/2 a' (2t)^2 = 2a' t^2
Time taken, 2t = √(2d/a')
As per the given condition, 2t = 2t x (3/2)
=> √(2d/a') = (3/2) √(2d/a)
=> a'/a = 9/4
=> g sin 45o - µg cos 45o = (9/4) g sin 45o
=> µ = (3/4)
Therefore, the coefficient of friction is 3/4. Answer: (a).
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A block takes twice as much time to slide down a 45o rough inclined plane as it takes to slide down a similar smooth plane. The coefficient of friction is a)3/4b)3/2c)1/4d)1/3Correct answer is option 'A'. 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 block takes twice as much time to slide down a 45o rough inclined plane as it takes to slide down a similar smooth plane. The coefficient of friction is a)3/4b)3/2c)1/4d)1/3Correct answer is option 'A'. 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 block takes twice as much time to slide down a 45o rough inclined plane as it takes to slide down a similar smooth plane. The coefficient of friction is a)3/4b)3/2c)1/4d)1/3Correct answer is option 'A'. Can you explain this answer?.
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