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A plumb Bob of mass 1kg is hung from the ceiling of train compartment the train moves on an inclined plane wd constant velocity if the angle of incline is 30 find angle made by string wd normal to the cieling also find tension in string?
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A plumb Bob of mass 1kg is hung from the ceiling of train compartment ...
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A plumb Bob of mass 1kg is hung from the ceiling of train compartment ...
Angle made by string with normal to the ceiling:
To find the angle made by the string with the normal to the ceiling, we need to consider the forces acting on the plumb bob.
Forces acting on the plumb bob:
1. Weight (mg): The weight of the plumb bob acts vertically downwards.
2. Tension (T): The tension in the string acts along the length of the string.
Resolving forces:
Since the train is moving on an inclined plane with constant velocity, the plumb bob is in a state of equilibrium. Therefore, the net force acting on the plumb bob is zero.
We can resolve the weight of the plumb bob into two components: one parallel to the incline and the other perpendicular to the incline. The component perpendicular to the incline balances out the normal force exerted by the ceiling, while the component parallel to the incline is counteracted by the tension in the string.
Angle made by the string:
The angle made by the string with the normal to the ceiling is equal to the angle of incline of the plane, which is given as 30 degrees.
Tension in the string:
To find the tension in the string, we need to consider the vertical and horizontal components of the forces acting on the plumb bob.
Vertical component:
The vertical component of the tension balances out the weight component perpendicular to the incline. Using trigonometry, we can determine this component as T * cos(30).
Horizontal component:
The horizontal component of the tension balances out the weight component parallel to the incline. Using trigonometry, we can determine this component as T * sin(30).
Equilibrium condition:
Since the plumb bob is in equilibrium, the vertical and horizontal components of the tension must be equal to the corresponding weight components. Therefore, we have the following equations:
T * cos(30) = mg * cos(30)
T * sin(30) = mg * sin(30)
Solving for tension:
From the equations above, we can solve for T:
T = (mg * cos(30)) / cos(30)
T = mg
Therefore, the tension in the string is equal to the weight of the plumb bob, which is 1 kg multiplied by the acceleration due to gravity (9.8 m/s^2), resulting in a tension of 9.8 N.
In summary, the angle made by the string with the normal to the ceiling is 30 degrees, and the tension in the string is 9.8 N.
To find the angle made by the string with the normal to the ceiling, we need to consider the forces acting on the plumb bob.
Forces acting on the plumb bob:
1. Weight (mg): The weight of the plumb bob acts vertically downwards.
2. Tension (T): The tension in the string acts along the length of the string.
Resolving forces:
Since the train is moving on an inclined plane with constant velocity, the plumb bob is in a state of equilibrium. Therefore, the net force acting on the plumb bob is zero.
We can resolve the weight of the plumb bob into two components: one parallel to the incline and the other perpendicular to the incline. The component perpendicular to the incline balances out the normal force exerted by the ceiling, while the component parallel to the incline is counteracted by the tension in the string.
Angle made by the string:
The angle made by the string with the normal to the ceiling is equal to the angle of incline of the plane, which is given as 30 degrees.
Tension in the string:
To find the tension in the string, we need to consider the vertical and horizontal components of the forces acting on the plumb bob.
Vertical component:
The vertical component of the tension balances out the weight component perpendicular to the incline. Using trigonometry, we can determine this component as T * cos(30).
Horizontal component:
The horizontal component of the tension balances out the weight component parallel to the incline. Using trigonometry, we can determine this component as T * sin(30).
Equilibrium condition:
Since the plumb bob is in equilibrium, the vertical and horizontal components of the tension must be equal to the corresponding weight components. Therefore, we have the following equations:
T * cos(30) = mg * cos(30)
T * sin(30) = mg * sin(30)
Solving for tension:
From the equations above, we can solve for T:
T = (mg * cos(30)) / cos(30)
T = mg
Therefore, the tension in the string is equal to the weight of the plumb bob, which is 1 kg multiplied by the acceleration due to gravity (9.8 m/s^2), resulting in a tension of 9.8 N.
In summary, the angle made by the string with the normal to the ceiling is 30 degrees, and the tension in the string is 9.8 N.
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A plumb Bob of mass 1kg is hung from the ceiling of train compartment the train moves on an inclined plane wd constant velocity if the angle of incline is 30 find angle made by string wd normal to the cieling also find tension in string?
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A plumb Bob of mass 1kg is hung from the ceiling of train compartment the train moves on an inclined plane wd constant velocity if the angle of incline is 30 find angle made by string wd normal to the cieling also find tension in string? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A plumb Bob of mass 1kg is hung from the ceiling of train compartment the train moves on an inclined plane wd constant velocity if the angle of incline is 30 find angle made by string wd normal to the cieling also find tension in string? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A plumb Bob of mass 1kg is hung from the ceiling of train compartment the train moves on an inclined plane wd constant velocity if the angle of incline is 30 find angle made by string wd normal to the cieling also find tension in string?.
A plumb Bob of mass 1kg is hung from the ceiling of train compartment the train moves on an inclined plane wd constant velocity if the angle of incline is 30 find angle made by string wd normal to the cieling also find tension in string? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A plumb Bob of mass 1kg is hung from the ceiling of train compartment the train moves on an inclined plane wd constant velocity if the angle of incline is 30 find angle made by string wd normal to the cieling also find tension in string? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A plumb Bob of mass 1kg is hung from the ceiling of train compartment the train moves on an inclined plane wd constant velocity if the angle of incline is 30 find angle made by string wd normal to the cieling also find tension in string?.
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