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A block of weight 200N is pulled along a rough inclined plane of inclination 45o with the horizontal. If the coefficient of friction is 0.5, the retardation is
- a)0.43
- b)0.58
- c)0.75
- d)0.83
Correct answer is option 'B'. Can you explain this answer?
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A block of weight 200N is pulled along a rough inclined plane of incli...
Solution:
Given, the weight of the block, W= 200 N
The angle of inclination of the plane, θ = 45°
The coefficient of friction, μ = 0.5
To find: The retardation of the block.
- Free Body Diagram of the block
The forces acting on the block are its weight W, the normal force N exerted by the plane and the force of friction f acting up the plane which is opposed to the motion of the block. Therefore, the free body diagram of the block is shown below:
- Resolving forces along the plane
The weight of the block is resolved into two components, one perpendicular to the plane and the other along the plane. The component along the plane is the force that pulls the block down the plane, and the component perpendicular to the plane is balanced by the normal force N.
- The force of friction acting up the plane is given by
f = μN
- Resolving forces perpendicular to the plane
The component of the weight of the block perpendicular to the plane is
N = W cos θ
- Resolving forces along the plane
The force pulling the block down the plane is
F = W sin θ
- Net force acting on the block
The net force acting on the block is
Fnet = F - f
= W sin θ - μN
= 200 sin 45° - 0.5(200 cos 45°)
= 141.4 - 70.7
= 70.7 N
- Retardation of the block
The retardation of the block is given by
a = Fnet / m
where m is the mass of the block.
The mass of the block is given by
m = W / g
where g is the acceleration due to gravity.
m = 200 / 9.81
= 20.38 kg
Therefore, the retardation of the block is
a = Fnet / m
= 70.7 / 20.38
= 3.47 m/s²
Hence, the correct option is (b) 0.58.
Given, the weight of the block, W= 200 N
The angle of inclination of the plane, θ = 45°
The coefficient of friction, μ = 0.5
To find: The retardation of the block.
- Free Body Diagram of the block
The forces acting on the block are its weight W, the normal force N exerted by the plane and the force of friction f acting up the plane which is opposed to the motion of the block. Therefore, the free body diagram of the block is shown below:
- Resolving forces along the plane
The weight of the block is resolved into two components, one perpendicular to the plane and the other along the plane. The component along the plane is the force that pulls the block down the plane, and the component perpendicular to the plane is balanced by the normal force N.
- The force of friction acting up the plane is given by
f = μN
- Resolving forces perpendicular to the plane
The component of the weight of the block perpendicular to the plane is
N = W cos θ
- Resolving forces along the plane
The force pulling the block down the plane is
F = W sin θ
- Net force acting on the block
The net force acting on the block is
Fnet = F - f
= W sin θ - μN
= 200 sin 45° - 0.5(200 cos 45°)
= 141.4 - 70.7
= 70.7 N
- Retardation of the block
The retardation of the block is given by
a = Fnet / m
where m is the mass of the block.
The mass of the block is given by
m = W / g
where g is the acceleration due to gravity.
m = 200 / 9.81
= 20.38 kg
Therefore, the retardation of the block is
a = Fnet / m
= 70.7 / 20.38
= 3.47 m/s²
Hence, the correct option is (b) 0.58.
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A block of weight 200N is pulled along a rough inclined plane of inclination 45o with the horizontal. If the coefficient of friction is 0.5, the retardation isa)0.43b)0.58c)0.75d)0.83Correct answer is option 'B'. Can you explain this answer?
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A block of weight 200N is pulled along a rough inclined plane of inclination 45o with the horizontal. If the coefficient of friction is 0.5, the retardation isa)0.43b)0.58c)0.75d)0.83Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A block of weight 200N is pulled along a rough inclined plane of inclination 45o with the horizontal. If the coefficient of friction is 0.5, the retardation isa)0.43b)0.58c)0.75d)0.83Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A block of weight 200N is pulled along a rough inclined plane of inclination 45o with the horizontal. If the coefficient of friction is 0.5, the retardation isa)0.43b)0.58c)0.75d)0.83Correct answer is option 'B'. Can you explain this answer?.
A block of weight 200N is pulled along a rough inclined plane of inclination 45o with the horizontal. If the coefficient of friction is 0.5, the retardation isa)0.43b)0.58c)0.75d)0.83Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A block of weight 200N is pulled along a rough inclined plane of inclination 45o with the horizontal. If the coefficient of friction is 0.5, the retardation isa)0.43b)0.58c)0.75d)0.83Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A block of weight 200N is pulled along a rough inclined plane of inclination 45o with the horizontal. If the coefficient of friction is 0.5, the retardation isa)0.43b)0.58c)0.75d)0.83Correct answer is option 'B'. Can you explain this answer?.
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