MHT CET202519 Apr 2025Morning ShiftPhysicsOscillationsActual
' P ' and ' Q ' are fixed points in same plane and mass ' m ' is tied by string as shown in figure. If the mass is displaced slightly out of this plane and released, it will oscillate with time period ( PQ =2 ~d , PR = QR = L ) (g=gravitational acceleration)
Options
- A2 L g
- B2 L^2 g
- C2 (L^2-d^2 )^ 1 / 2 g
- D2 (L^2+d^2 )^ 1 / 2 g
Correct answer
C. 2 (L^2-d^2 )^ 1 / 2 g
Step-by-step solution
The oscillation occurs in a plane perpendicular to line PQ with an effective pendulum length equal to the vertical distance from the midpoint M of PQ to the equilibrium position R . For triangle PMR , where PR = L and PM = d , applying the Pythagorean theorem yields MR = L^2 - d^2 . The period for small oscillations is given by the standard pendulum formula with this effective length: T = 2 L^2 - d^2 g This corresponds to option C .