Q. 15

# 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 υ 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.

C.

D. zero

Answer :

During the jump of the car from the cliff its path resembles a parabola. Its trajectory is like a projectile and from its

highest position is freely falling under gravity with an acceleration g acting downward. Here, it is a non- inertial frame of reference. So a pseudo force equal to mg has to be applied to the bob in upward direction which neutralizes the weight acting and balancing it out. So the tension in the string is zero.

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The displacement vector of a particle of mass m is given by r (t) = î A cos ωt + ĵ B sin ωt.

(a) Show that the trajectory is an ellipse.

(b) Show that F = −mω^{2}r

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