Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Problem 149

Pressure \(P=A \cos B x+c \sin D t\) where \(x\) in meter and \(t\) in time then find dimensional formula of \(\mathrm{D} / \mathrm{B}\) (a) \(\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-1}\) (b) \(\mathrm{M}^{0} \mathrm{~L}^{1} \mathrm{~T}^{-1}\) (c) \(\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{0}\) (d) \(\mathrm{M}^{-1} \mathrm{~L}^{0} \mathrm{~T}^{1}\)

Short Answer

Expert verified
\(M^0 L^1 T^1\)

Step by step solution

01

Determine dimensional formula of given variables

We are given: - Pressure P is in M L^-1 T^-2 (mass, length, time) - Position x is in L (length) - Time t is in T (time)
02

Analyze the given formula for Pressure

The given formula for pressure is: P = A cos(Bx) + C sin(Dt) We know that the dimensions of P are M L^-1 T^-2. Now, let's find the dimensions for A, B, C, and D.
03

Determine dimensions of A and C

Since A cos(Bx) and C sin(Dt) have the same dimensions (pressure), we can say that both A and C have the same dimensions as pressure: A and C have dimensions of: M L^-1 T^-2
04

Determine dimensions of B and D

Now, let's find the dimensions of B and D. Since cosine and sine functions are dimensionless, we need to ensure that the arguments Bx and Dt are dimensionless as well. This means that the dimension of B multiplied by the dimension of x must be equal to the dimension of D multiplied by the dimension of t. Since x has dimensions L, and t has dimensions T: - B has dimensions L^-1, ensuring that Bx is dimensionless - D has dimensions T^-1, ensuring that Dt is dimensionless
05

Find the dimensional formula of D / B

Now that we know the dimensions of D and B, we can find the dimensions of the ratio D/B: Dimensions of D/B = (T^-1) / (L^-1) = T^1 L^1 Thus, the dimensional formula of D/B is \(M^0 L^1 T^1\). So, our final answer is: (b) \(\mathrm{M}^{0}\mathrm{~L}^{1}\mathrm{~T}^{-1}\)

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

In an experiment to determine the density of a cube the percentage error in the measurement of mass is \(0.25 \%\) and the percentage error in the measurement of length is \(0.50 \%\) what will be the percentage error in the determination of its density? (a) \(2.75 \%\) (b) \(1.75 \%\) (c) \(0.75 \%\) (d) \(1.25 \%\)

Equation of force \(F=a t+b t^{2}\) where \(F\) is force in Newton \(t\) is time in second, then write unit of \(\mathrm{b}\). (a) \(\mathrm{Ns}^{-1}\) (b) \(\mathrm{Ns}^{2}\) (c) \(\mathrm{Ns}\) (d) \(\mathrm{Ns}^{-2}\)

Dimensional formula for thermal conductivity (k) is.. (a) \(\mathrm{M}^{2} \mathrm{~L}^{1} \mathrm{~T}^{-2} \mathrm{~K}^{-1}\) (b) \(\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-2} \mathrm{~K}^{1}\) (c) \(\mathrm{M}^{1} \mathrm{~L}^{0} \mathrm{~T}^{-3} \mathrm{~K}^{-1}\) (d) \(\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-3} \mathrm{~K}^{-1}\)

Heat produced in a current carrying conducting wire is \(\mathrm{H}=\mathrm{I}^{2} \mathrm{Rt}\) it percentage error in $\mathrm{I}, \mathrm{R}\( and \)\mathrm{t}\( is \)2 \%, 4 \%\( and \)2 \%$ respectively then total percentage error in measurement of heat energy \(\ldots \ldots \ldots\) (a) \(8 \%\) (b) \(15 \%\) (c) \(5 \%\) (d) \(10 \%\)

If the centripetal force is of the form $\mathrm{m}^{\mathrm{a}} \mathrm{v} \mathrm{b}_{\mathrm{r}}^{\mathrm{c}}$ find the values of \(\mathrm{a}, \mathrm{b}\) and \(\mathrm{c}\) (a) \(1,2,1\) (b) \(1,2,-1\) \(\begin{array}{ll}\text { (c) } 1,3,-2 & \text { (d) }-1,3,-1\end{array}\)
See all solutions

Recommended explanations on English Textbooks

Single Paragraph Essay

Read Explanation

5 Paragraph Essay

Read Explanation

Argumentative Essay

Read Explanation

Rhetorical Analysis Essay

Read Explanation

Sociolinguistics

Read Explanation

English Grammar Summary

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