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

step 1 In this question it is given that a car is moving in a circular horizontal track of radius 10 me

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 $10 \mathrm{~m} / \mathrm{sec}$. 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: (Take $\left.g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$ (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 $10 \mathrm{~m} / \mathrm{sec}$. 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: (Take $\left.g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
(a) zero
(b) $30^{\circ}$
(c) $45^{\circ}$
(d) $60^{\circ}$

Key Concepts

Effective Gravity in Non-Inertial Frames

When analyzing motions in accelerating systems, such as a car turning along a circular path, the apparent or effective gravity is a combination of the real gravitational acceleration and the acceleration due to the motion of the frame (centripetal acceleration). This effective gravitational field determines the direction in which objects inside the accelerating frame, like a suspended rod, will align.

Vector Addition of Accelerations

Determining the orientation of objects in non-inertial frames involves the vector addition of accelerations. By combining the gravitational acceleration vector with the centripetal acceleration vector, one obtains an effective acceleration vector. The angle between this resultant vector and the vertical (or any reference direction) indicates how the object will incline in order to balance the net forces acting on it.

Centripetal Acceleration

Centripetal acceleration is the acceleration required for an object to keep moving in a circular path. Its magnitude is given by the formula a = v²/r, where v is the speed and r is the radius of the circle. This concept is crucial in analyzing forces acting on objects in circular motion.

Circular Motion

Circular motion involves an object moving along a curved path. In this type of motion, even if the speed is constant, there is always an acceleration because the direction of the velocity vector is changing. This acceleration, known as centripetal acceleration, acts perpendicular to the velocity and toward the center of the circle.

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