Question

A simple pendulum having a bob of mass, $m$, is suspended from the ceiling of a car used in a stunt film shooting. The car moves up along an inclined cliff at a speed $v$ and makes a jump to leave the cliff and lands at some distance. Let $R$ be the maximum height of the car from the top of the cliff. The tension in the string when the car is in air is:
A. mg
B. $mg - \dfrac{{m{v^2}}}{R}$
C. $mg + \dfrac{{m{v^2}}}{R}$
D. Zero

Answer 1

Another mechanical device that travels in an oscillating motion is the simple pendulum. It comprises a point mass $m$ hung from a fixed support by a light inextensible string of length $L$. The motion takes place in a vertical plane and is propelled by gravity.

Complete answer:
A trajectory, also known as a flight path, is the path taken by a mass in motion through space as a function of time. A trajectory is determined by Hamiltonian mechanics via canonical coordinates in classical mechanics; hence, a full trajectory is defined by position and momentum at the same time.

The route travelled by a paper aircraft as it travels through the air is an example of trajectory. When the automobile is in the air, the bob seems to be weightless, as if the string has no mass attached to it. As a result, there is no tension in the string at that point.The lack of the sense of weight is referred to as weightlessness. This is also referred to as zero-G, however the more accurate phrase is "zero G-force." It happens when there are no contact forces between items, including the human body.

During the car's jump from the cliff, its trajectory is similar to that of a projectile, and it falls freely under gravity with an acceleration of g downhill from the greatest height. It is a non-inertial frame of reference when used as a reference point. As a result, a fake force of mg must be given to the bob in an upward direction, neutralising the weight and reducing it to zero. As a result, there is no tension in the string.

Hence, the correct answer is option D.

Note: Here we have considered the acceleration due to gravity to find the tension of the string but sometimes we don't consider acceleration due to gravity for very small mass particles for easy calculation. Also we need to take care of all forces while calculating the tension of the string if there are any acting on the system.