A particle of mass M is suspended by two ideal strings as shown in the figure. Now, mass M is given a small displacement perpendicular to the plane of triangle formed. Choose the correct statement(s).
A
The period of oscillation of the system is 2π√3√3lg
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B
The period of oscillation of the system is 2π√3lg
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C
The period of oscillation of the system is independent of M.
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D
If the distance between the suspension points was kept constant and the lengths of the strings were quadrupled, then the period of the system will double.
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Solution
The correct option is C The period of oscillation of the system is independent of M.
x2=(5l)2−y2.....(1) (7l−x)2=(3√2l)2−y2.....(2),
From equation (1) and (2), x2−(7l−x)2=25l2−18l2 x2−(7l)2−x2+2x(7l)=25l2−18l2 2x−(7l)=l x=4l
Now, from equation (1) y2=(5l)2−(4l)2 y2=(3l)2 y=3l
We know that time period of oscillation is given by T=2π√yg
Substituting the value of y, we get T=2π√3lg
So, time period of oscillation of the system is independent of M.