MHT CET20243 May 2024Morning ShiftPhysicsOscillationsActual
A tube of uniform bore of cross-sectional area ' A ' has been set up vertically with open end facing up. Now 'M' gram of a liquid of density ' d ' is poured into it. The column of liquid in this tube will oscillate with a period ' T ', which is equal to [ g = acceleration due to gravity]
Options
- A2 MA gd
- B2 M 2 Adg
- C2 M g
- D2 M g d A
Correct answer
B. 2 M 2 Adg
Step-by-step solution
For a depression of y cm on one side, the level of liquid will be 2 y cm higher on the other side. Weight of extra liquid on the P -side =2 Aydg The above weight acts as the restoring force acting on mass M . Restoring acceleration =- 2 Aydg M (- ve sign indicates the acceleration and force are opposite to each other) ... (i) We know for simple harmonic motion, a=- ( k m ) x Comparing (i) and (ii), we see the motion is simple harmonic. aligned T & =2 Displacement Acceleration =2 y 2 Aydg M & =2 M 2 Adg aligned