Q. 16

# Let θ denote the angular displacement of a simple pendulum oscillating in a vertical plane. If the mass of the bob is m, the tension in the string is mg cosθ

A. always

B. never

C. at the extreme positions

D. at the mean position

Answer :

Tension in a string at any position is given as , where r is the length of pendulum and v is the instantaneous velocity of the bob. Now at the extremes points velocity of the bob is zero. Hence the term nullifies leaving alone . So, the tension in the string at extreme points is .

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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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