Q16 of 63 Page 114

Suppose the amplitude of a simple pendulum having a bob of mass m is θ0. Find the tension in the string when the bob is at its extreme position.


When a simple pendulum reaches the extreme position it stops at that point. That means



So, the centrifugal force will become,




So, the only force that is going to contribute to tension will be the component of gravity opposite to the direction of tension.


So, tension will be,



More from this chapter

All 63 →
14

The bob of a simple pendulum of length 1 m has mass loo g and a speed of 1.4 m/s at the lowest point in its path. Find the tension in the string at this instant.

 15

Suppose the bob of the previous problem has a speed of 1.4 m/s when the string makes an angle of 0.20 radian with the vertical. Find the tension at this instant. You can use ≈ cosθ ≈ 1 - θ2/2 and sinθ ≈ θ, for small θ.

 17

A person stands on a spring balance at the equator. (a) By what fraction is the balance reading less than his true weight? (b) If the speed of earth’s rotation is increased by such an amount that the balance reading is half the true weight, what will be the length of the day in this case?

 18

A turn of radius 20 in is banked for the vehicles going at a speed of 36 km/h. If the coefficient of static friction between the road and the tyre is 0.4, what are the possible speeds of a vehicle so that it neither slips down nor skids up?