CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half-submerged in a liquid of density at the equilibrium position. The extension x0 of the spring when it is in equilibrium is?


Open in App
Solution

Extension of spring:

Extension springs are used to absorb and store energy while also providing resistance to a pulling force.

Step 1: Given:

  1. Length of cylinder = L
  2. Mass of cylinder = M
  3. Cross Sectional area of cylinder = A

Step 2: Formula Used:

kxo+FB=Mg

Here, kxo is stress on spring, FB is buoyant force, M is mass, and g is acceleration due to gravity.

Step 3: Calculating extension xo

The figure shows the various forces acting on the cylinder.

Mg is the weight of the cylinder, FB is buoyant force, and kxo is stress on spring, xo is the extension in the string, and k is spring constant.

At equilibrium,
Upward forces = Downward forces

kxo+FB=Mg ------------- (i)

FB is the force due to buoyancy which is equal to the weight of the liquid displaced.

FB=σ·L2·A·g

Putting the value of FB in equation (i)

kxo+σ·L2·A·g=Mgxo=Mg-σ·L2·A·gkxo=Mgk1-σLA2M


flag
Suggest Corrections
thumbs-up
0
BNAT
mid-banner-image
similar_icon
Similar questions
View More