Two identical, thin rods, each with 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. if the l-shaped object is deflected slightly, it oscillates.

find the frequency of oscillation.

The frequency of oscillation of the given L-shaped object made of two rods is .

Further Explanation:

The combination of the two rods perpendicular to each other and making a L-shaped object is as shown in figure attached below.

This L-shaped object rests on a sharp edge and therefore, each rod will make an angle of  with the sharp edge. When there is a very small deflection in the rod, it will start performing oscillations with a small angle . Then the time period of oscillation of this rod about its center of gravity is given as:

                                      …… (1)

Here,  is the moment of inertia of the rod,  is the distance of the center of gravity from the fixed point and  is the time period of oscillation of the L-shaped object.

The moment of inertia of the rod about its one end is given as:

For the above mentioned case, the moment of inertia of the two rods about the fixed sharp point is:

The distance of the center of gravity from the fixed point is:

Substitute the values in equation (1).

The frequency of oscillation of the L-shaped object is:

Thus, the frequency of oscillation of the given L-shaped object made of two rods is

.

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Answer Details:

Grade: Senior School

Subject: Physics

Chapter: Simple Harmonic Motion

Keywords:

L-shaped object, two identical thin rods, balanced, a sharp edge, deflected slightly, moment of inertia, frequency of oscillation, center of gravity.

the answer is b

explanation: