# Balanced Triangular Loop in Magnetic Field

An equilateral triangular loop of mass $$M$$ and side $$a$$ at rest is under the influence of magnetic field B and gravitational field as shown in figure.

If the frame is slightly displaced in downward direction, the time period of small oscillations is given by

$$2\pi \sqrt{\dfrac{\sqrt{X}a}{Yg}}$$

Find $$X+Y$$

Details and assumptions

$$l = \frac{\sqrt{3}a}{4}$$

$$g$$ is acceleration due to gravity

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