Home
Class 11
PHYSICS
A plank of mass 'm' and area of cross - ...

A plank of mass 'm' and area of cross - section `A` is floating in a non - viscous liquid of desity `rho`. When displaced slightly from the mean position, it starts oscillating. Prove that oscillations are simple harmonic and find its time period.

Text Solution

Verified by Experts

The correct Answer is:
A, B
Two forces are action on the plank: weight and upthrust. Weight is a constant force. So, forget it. Upthrust (if partially immersed ) is a variable force. When displaced downwards by a distance `x`, then
Net restoring force`F_(net) = - ["change or increase in variable force upthrust"]`
= - [(extra immersed volume) (density of liquid) (g)]
` = -[(Ax)(rho)(g)]`
This force is of type `F = - kx`
So, motion is simple harmonic, where `k = rho Ag`
`:. T = 2pi sqrt((m)/(k))` or `T = 2pi sqrt((m)/(rho Ag))`.
Promotional Banner

Topper's Solved these Questions

  • SIMPLE HARMONIC MOTION

    DC PANDEY|Exercise Miscellaneous Examples|8 Videos

  • SIMPLE HARMONIC MOTION

    DC PANDEY|Exercise Level 1 Assertion And Reason|10 Videos

  • SIMPLE HARMONIC MOTION

    DC PANDEY|Exercise Example Type 12|1 Videos

  • SEMICONDUCTORS AND ELECTRONIC DEVICES

    DC PANDEY|Exercise More than One Option is Correct|3 Videos

  • SOLVD PAPERS 2017 NEET, AIIMS & JIPMER

    DC PANDEY|Exercise Solved paper 2018(JIPMER)|38 Videos

Similar Questions

Explore conceptually related problems

A plank of mass 'm' and area of cross - section A is floating as shown in figure. When slightly displaced from mean position, plank starts oscillations. Find time period of these osillations.

A cylinderical block of wood of mass m and area cross-section A is floating in water (density = rho ) when its axis vertical. When dressed a little and the released the block starts oscillating. The period oscillations is

A rectangular block of mass m and area of cross-section A floats in a liquid of density rho . If it is given a small vertical displacement from equilibrium, it undergoes oscillation with a time period T. Then

Starting from the mean position a body oscillates simple harmonically with a period of 2 s.

A rectangular block of mass m and area of cross-section A floats in a liquid of density rho . If it is givan a small vertical displacement from equilibrium, it undergoes oscillation with a time period T, then select the wrong alternative.

A block of rectangular size of mass m and area of cross section A, float in a liquid of density rho .If we give a small vertical displacement from equilibrium, It undergoes SHM with time period T, then