Question

: A plumb line is suspended from a ceiling of a car moving with horizontal acceleration of a. What will be the angle of inclination with vertical.
A. \[{\tan ^{ - 1}}\left( {a/g} \right)\]
B. \[{\tan ^{ - 1}}\left( {g/a} \right)\]
C. \[{\cos ^{ - 1}}\left( {a/g} \right)\]
D. \[{\cos ^{ - 1}}\left( {g/a} \right)\]

Answer 1

Hint:The above problem is resolved by applying the concept and application of the banking of the road. The banking of the road is one of the major phenomena considered to determine the value of any vehicle's velocity in a curved road. Moreover, there is some angle of inclination for the tilt that is to be calculated accordingly.

Complete step by step answer:
The car moving the horizontal direction with the magnitude of acceleration a, one can observe the plumb line's suspension through the ceiling of the car. And this suspension of the plumb line will cause the tilt due to the magnitude of the pseudo force on the plumb line. And the tilt is given through an angle known as the angle of tilt.
We know the standard formula for the angle of tilt is given as,
\[\tan \theta = \dfrac{a}{g}\]
Here, a is the magnitude of acceleration and g is the magnitude of acceleration due to gravity which is experienced because of the tilting.
Then, the above expression can be written as,
\[\begin{array}{l}
\tan \theta = \dfrac{a}{g}\\
\theta = {\tan ^{ - 1}}\left( {a/g} \right)
\end{array}\]
Therefore, the angle of inclination with vertical is \[{\tan ^{ - 1}}\left( {a/g} \right)\] and option (A) is correct.

Note: Try to understand the concept of the centripetal force and the applications of the centripetal force. The centripetal force is that force acting along the curved path while an object is in motion through that path. Moreover, this creates a major application in analysing the banking of roads.