Question

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 $2\pi \sqrt{\frac{3\sqrt{3}l}{g}}$
• B. The period of oscillation of the system is $2\pi \sqrt{\frac{3l}{g}}$
• C. The period of oscillation of the system is independent of M.
• 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.

Answer 1

Answer: (B), (C)

The period of oscillation of the system is independent of M.


$x^2=(5l{)}^2-y^2.....(1)$
$(7l-x{)}^2=(3\sqrt{2}l{)}^2-y^2.....\left(2\right)$,
From equation (1) and (2),
$x^2-(7l-x{)}^2=25l^2-18l^2$
$x^2-(7l{)}^2-x^2+2x(7l)=25l^2-18l^2$
$2x-\left(7l\right)=l$
$x=4l$
Now, from equation (1)
$y^2=(5l{)}^2-(4l{)}^2$
$y^2=(3l{)}^2$
$y=3l$
We know that time period of oscillation is given by
$T=2\pi \sqrt{\frac{y}{g}}$
Substituting the value of y, we get
$T=2\pi \sqrt{\frac{3l}{g}}$
So, time period of oscillation of the system is independent of M.