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A plumb line is suspended from a ceiling of a ear moving with horizontal acceleration of a. What will be the angle of inclination with vertical?
- a)tan⁻1(a/g)
- b)tan⁻1(g/a)
- c)cos⁻1(a/g)
- d)cos⁻1(g/a)
Correct answer is option 'A'. Can you explain this answer?
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A plumb line is suspended from a ceiling of a ear moving with horizont...
Given:
- Ceiling of a car is moving with horizontal acceleration a.
- A plumb line is suspended from the ceiling.
To find:
- The angle of inclination with the vertical.
Solution:
Let's consider the forces acting on the plumb line:
- Weight of the plumb line acting downwards, which is balanced by the tension in the string.
- Inertial force acting towards the direction of acceleration a.
The angle of inclination with the vertical can be found by resolving the forces acting on the plumb line.
- The weight of the plumb line acts vertically downwards, so it can be resolved into two components:
- One component acting along the string which balances the tension in the string.
- The other component acting perpendicular to the string, which is responsible for the angle of inclination.
- The inertial force acts horizontally, so it can be resolved into two components:
- One component acting along the string in the opposite direction to the weight of the plumb line.
- The other component acting perpendicular to the string, which is responsible for the angle of inclination.
From the above analysis, it is clear that the angle of inclination is equal to the angle between the direction of acceleration and the vertical.
From trigonometry, we know that:
- tan(theta) = perpendicular/base
- base = g (acceleration due to gravity)
- perpendicular = a (horizontal acceleration)
Therefore, the angle of inclination, theta = tan^-1(a/g)
Hence, the correct answer is option 'A'.
- Ceiling of a car is moving with horizontal acceleration a.
- A plumb line is suspended from the ceiling.
To find:
- The angle of inclination with the vertical.
Solution:
Let's consider the forces acting on the plumb line:
- Weight of the plumb line acting downwards, which is balanced by the tension in the string.
- Inertial force acting towards the direction of acceleration a.
The angle of inclination with the vertical can be found by resolving the forces acting on the plumb line.
- The weight of the plumb line acts vertically downwards, so it can be resolved into two components:
- One component acting along the string which balances the tension in the string.
- The other component acting perpendicular to the string, which is responsible for the angle of inclination.
- The inertial force acts horizontally, so it can be resolved into two components:
- One component acting along the string in the opposite direction to the weight of the plumb line.
- The other component acting perpendicular to the string, which is responsible for the angle of inclination.
From the above analysis, it is clear that the angle of inclination is equal to the angle between the direction of acceleration and the vertical.
From trigonometry, we know that:
- tan(theta) = perpendicular/base
- base = g (acceleration due to gravity)
- perpendicular = a (horizontal acceleration)
Therefore, the angle of inclination, theta = tan^-1(a/g)
Hence, the correct answer is option 'A'.
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A plumb line is suspended from a ceiling of a ear moving with horizontal acceleration of a. What will be the angle of inclination with vertical?a)tan1(a/g)b)tan1(g/a)c)cos1(a/g)d)cos1(g/a)Correct answer is option 'A'. Can you explain this answer?
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