Q.

Three masses of small size are attached by light inextensible strings of various lengths to a point O on the ceiling. All of the masses swing roundin horizontal circles of various radii with the same angular frequency ω (one such circle is drawn in the shown figure.) Then pick up the correct statement.

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a

The vertical depth of each mass below point of suspension from ceiling is different.

b

The radius of horizontal circular path of each mass is same.

c

All masses revolve in the same horizontal plane.

d

All the particles must have same mass.

answer is .

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Detailed Solution

For conical pendulum of length λ mass m moving along horizontal circle as shownT cos θ = mg-------------(i)T sin θ = mω2l sin θ--------(ii)From equation (i) and equation (ii),l cos θ = gω2l cos θ is the vertical distance of bob below O point of suspension. Hence if ω of all three pendulums are same, they shall revolve in same horizontal plane.
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