Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Problem 1007

A vesel whose bottom has round holes with diameter of \(0.1 \mathrm{~mm}\) is filled with water. The maximum height to which the water can be filled without leakage is (S.T. of water \(=[(75\) dyne $\left.\\} / \mathrm{cm}], \mathrm{g}=1000 \mathrm{~m} / \mathrm{s}^{2}\right)$ (A) \(100 \mathrm{~cm}\) (B) \(75 \mathrm{~cm}\) (C) \(50 \mathrm{~cm}\) (D) \(30 \mathrm{~cm}\)

Short Answer

Expert verified
The maximum height to which the water can be filled without leakage is \(75 \mathrm{~cm}\).

Step by step solution

01

Write the expression for surface tension force

The force due to surface tension (F) is given by the product of the surface tension (S) and the circumference of the hole: F = S × 2πr Where, r is the radius of the hole.
02

Calculate the radius

Calculate the radius (r) from the given diameter of the hole (0.1 mm): r = diameter/2 = 0.1/2
03

Convert units

Convert the units of r from millimeters to centimeters: r = 0.1/2 × (1/10) = 0.005 cm
04

Write the expression for gravitational force

Gravitational force (F') is given by the product of volume, density (ρ), and acceleration due to gravity (g): F' = Vρg Where, V is the volume of the water cylinder inside the hole.
05

Write the expression for volume

Write the volume (V) of the water cylinder as the product of the cross-sectional area of the hole and the maximum height (H) of the water: V = πr^2H
06

Write the conditions for balance between forces

At equilibrium, the gravitational force (F') must be equal to the surface tension force (F): S × 2πr = πr^2Hρg
07

Solve for H

Divide both sides by πr and the given values for S, ρ and g to solve for H: H = \(\frac{(2S)}{rρg}\) = \(\frac{150~\text{dyne/cm} × 2}{0.005~\text{cm} × 1~\text{g/cm}^{3} × 1000~\text{cm/s}^2}\) H = 75 cm The correct answer is (B) \(75 \mathrm{~cm}\). The maximum height to which the water can be filled without leakage is 75 cm.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

For a constant hydraulic stress on an object, the fractional change in the object volume \([\Delta \mathrm{V} / \mathrm{V}]\) and its bulk modulus (B) are related as............ (A) \((\Delta \mathrm{V} / \mathrm{V}) \alpha \beta\) (B) \((\Delta \mathrm{V} / \mathrm{V}) \alpha \beta^{-1}\) (C) \((\Delta \mathrm{V} / \mathrm{V}) \alpha \beta^{2}\) (D) \((\Delta \mathrm{V} / \mathrm{V}) \alpha \beta^{-2}\)

Two solid spheres of same metal but of mass \(\mathrm{M}\) and \(8 \mathrm{M}\) full simultaneously on a viscous liquid and their terminal velocity are \(\mathrm{V}\) and ' \(\mathrm{nV}^{\prime}\) then value of 'n' is (A) 16 (B) 8 (C) 4 (D) 2

Read the assertion and reason carefully to mark the correct option out of the option given below. (a) If both assertion and reason are true and the reason is the correct explanation of the reason. (b) If both assertion and reason are true but reason is not the correct explanation of the assertion. (c) If assertion is true but reason is false. (d) If the assertion and reason both are false. (e) If assertion is false but reason is true. Assertion: Specific heat capacity is the cause of formation of land and sea breeze. Reason: The specific heat of water is more then land. (A) a (B) \(b\) (C) \(c\) (D) \(\mathrm{d}\) \((\mathrm{E}) \mathrm{e}\)

The excess of pressure inside a soap bubble than that of the outer pressure is (A) \((2 \mathrm{~T} / \mathrm{r})\) (B) \((4 \mathrm{~T} / \mathrm{r})\) (C) \((\mathrm{T} / 2 \mathrm{r})\) (D) \((\mathrm{T} / \mathrm{r})\)

Two drops of the same radius are falling through air with a steady velocity for \(5 \mathrm{~cm}\) per sec. If the two drops coakesce the terminal velocity would be (A) \(10 \mathrm{~cm}\) per sec (B) \(2.5 \mathrm{~cm}\) per sec (C) \(5 \times(4)^{(1 / 3)} \mathrm{cm}\) per sec (D) \(5 \times \sqrt{2} \mathrm{~cm}\) per sec
See all solutions

Recommended explanations on English Textbooks

Multiple Choice Questions

Read Explanation

5 Paragraph Essay

Read Explanation

Phonetics

Read Explanation

Pragmatics

Read Explanation

Semiotics

Read Explanation

Cues and Conventions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free