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A body of mass 'm' is launched up on a rough inclined plane making an angle of 30° with the horizontal. The coefficient of friction between the body and plane is √x/5 if the time of ascent is half of the time of descent. The value of x is _______.
Correct answer is '3'. Can you explain this answer?
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A body of mass m is launched up on a rough inclined plane making an an...
With the horizontal. The coefficient of kinetic friction between the body and the inclined plane is μ. Find the acceleration of the body up the inclined plane.
To find the acceleration of the body up the inclined plane, we need to consider the forces acting on the body. There are two main forces acting on the body: the gravitational force and the frictional force.
1. Gravitational force: The gravitational force acting on the body can be split into two components: one parallel to the inclined plane (mg*sinθ) and one perpendicular to the inclined plane (mg*cosθ), where θ is the angle of the inclined plane.
2. Frictional force: The frictional force between the body and the inclined plane opposes the motion and is given by the equation f = μN, where N is the normal force acting on the body. The normal force can be split into two components: one perpendicular to the inclined plane (mg*cosθ) and one parallel to the inclined plane (mg*sinθ).
Now, let's calculate the net force acting on the body up the inclined plane:
Net force = Force parallel to the inclined plane - Force opposing motion
= mg*sinθ - μmg*cosθ
Using Newton's second law (F = ma), we can equate the net force to the mass of the body times its acceleration:
mg*sinθ - μmg*cosθ = ma
Now, we can solve this equation for acceleration:
a = (mg*sinθ - μmg*cosθ) / m
= g*sinθ - μg*cosθ
Therefore, the acceleration of the body up the inclined plane is given by a = g*sinθ - μg*cosθ.
To find the acceleration of the body up the inclined plane, we need to consider the forces acting on the body. There are two main forces acting on the body: the gravitational force and the frictional force.
1. Gravitational force: The gravitational force acting on the body can be split into two components: one parallel to the inclined plane (mg*sinθ) and one perpendicular to the inclined plane (mg*cosθ), where θ is the angle of the inclined plane.
2. Frictional force: The frictional force between the body and the inclined plane opposes the motion and is given by the equation f = μN, where N is the normal force acting on the body. The normal force can be split into two components: one perpendicular to the inclined plane (mg*cosθ) and one parallel to the inclined plane (mg*sinθ).
Now, let's calculate the net force acting on the body up the inclined plane:
Net force = Force parallel to the inclined plane - Force opposing motion
= mg*sinθ - μmg*cosθ
Using Newton's second law (F = ma), we can equate the net force to the mass of the body times its acceleration:
mg*sinθ - μmg*cosθ = ma
Now, we can solve this equation for acceleration:
a = (mg*sinθ - μmg*cosθ) / m
= g*sinθ - μg*cosθ
Therefore, the acceleration of the body up the inclined plane is given by a = g*sinθ - μg*cosθ.
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A body of mass m is launched up on a rough inclined plane making an an...
Using the above values of aa and ad and putting in equation (i), we will get
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A body of mass m is launched up on a rough inclined plane making an angle of 30° with the horizontal. The coefficient of friction between the body and plane is √x/5if the time of ascent is half of the time of descent. The value of x is _______.Correct answer is '3'. Can you explain this answer?
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A body of mass m is launched up on a rough inclined plane making an angle of 30° with the horizontal. The coefficient of friction between the body and plane is √x/5if the time of ascent is half of the time of descent. The value of x is _______.Correct answer is '3'. 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 body of mass m is launched up on a rough inclined plane making an angle of 30° with the horizontal. The coefficient of friction between the body and plane is √x/5if the time of ascent is half of the time of descent. The value of x is _______.Correct answer is '3'. 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 body of mass m is launched up on a rough inclined plane making an angle of 30° with the horizontal. The coefficient of friction between the body and plane is √x/5if the time of ascent is half of the time of descent. The value of x is _______.Correct answer is '3'. Can you explain this answer?.
A body of mass m is launched up on a rough inclined plane making an angle of 30° with the horizontal. The coefficient of friction between the body and plane is √x/5if the time of ascent is half of the time of descent. The value of x is _______.Correct answer is '3'. 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 body of mass m is launched up on a rough inclined plane making an angle of 30° with the horizontal. The coefficient of friction between the body and plane is √x/5if the time of ascent is half of the time of descent. The value of x is _______.Correct answer is '3'. 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 body of mass m is launched up on a rough inclined plane making an angle of 30° with the horizontal. The coefficient of friction between the body and plane is √x/5if the time of ascent is half of the time of descent. The value of x is _______.Correct answer is '3'. Can you explain this answer?.
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