A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m /

step 1 Hello students in this question we have a car which is moving in a circular horizontal track of

A car is moving in a circular horizontal track of radius 10...

A car is moving in a circular horizontal track of radius $10 \mathrm{~m}$ with a constant speed of $10 \mathrm{~m} / \mathrm{s}$. A plumb bob is suspended from the roof of the car by a light rigid rod of length $1 \mathrm{~m}$. The angle made by the rod with the track is: (a) zero (b) $30^{\circ}$ (c) $45^{\circ}$ (d) $60^{\circ}$

A car is moving in a circular horizontal track of radius $10 \mathrm{~m}$ with a constant speed of $10 \mathrm{~m} / \mathrm{s}$. A plumb bob is suspended from the roof of the car by a light rigid rod of length $1 \mathrm{~m}$. The angle made by the rod with the track is:
(a) zero
(b) $30^{\circ}$
(c) $45^{\circ}$
(d) $60^{\circ}$

Key Concepts

Non-Inertial Frames and Pseudo Forces

When an observer is in a non-inertial (accelerating) frame, fictitious or pseudo forces must be introduced to apply Newton’s laws. In the context of a car moving in a circle, a centrifugal pseudo force appears to act horizontally outward. This inertial effect, when combined with the gravitational force, determines the equilibrium position of objects like the plumb bob suspended inside the car.

Equilibrium of Forces and Resultant Acceleration

For an object in a non-inertial frame, the equilibrium position is determined by the vector sum of all the accelerations acting on it. In the case of the plumb bob, the gravitational acceleration acting downward and the centripetal acceleration acting horizontally towards the center of the circle combine to form a resultant effective acceleration. The bob aligns with this resultant direction, and the angle of deviation of the bob (with respect to the vertical or track) can be determined using trigonometric relationships, specifically the tangent function.

Circular Motion and Centripetal Acceleration

In circular motion, an object moving with constant speed is constantly accelerating towards the center of the circle. This acceleration, known as centripetal acceleration, has a magnitude of v²/r, where v is the speed and r is the radius of the circle. It is this acceleration that causes the deflection of objects in a non-inertial frame, such as the car, and is crucial for understanding the forces acting on the moving plumb bob.

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