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Two identical thin rods, each of mass m and length l, are joined at right angles to form an l-shaped object. This object is balanced on top of a sharp edge (figure 1). If the object is displaced slightly, it oscillates. Assume that the magnitude of the acceleration due to gravity is g.

Sagot :

The frequency of the oscillation is; (1/2π)√[3g/(L√2)]

We are given;

Mass of both identical rods = m

Length of both identical rods = L

The image of the 2 identical rods are missing and so i have attached it.

  • If the rods join at say an angle of 90°, then it means that moment of inertia of the combined system is;

I = ⅓mL² + ⅓mL²

I = ⅔mL²

  • Now, the effective length of the pendulum will be given as;

Eff. Length = L cos 45°

Thus; Eff. Length; l_eff = L/√2

Now, formula for time period is;

T = 2π√(I/Mgl_eff)

Where M is total mass = 2m

Thus:

T = 2π√(⅔mL²/(2gmL/√2)

T = 2π√[(L√2)/(3g)]

We know that frequency is; f = 1/T

Thus;

f = (1/2π)√[3g/(L√2)]

Read more about moment of inertia at; https://brainly.com/question/19548280

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