English
Karnataka Board PUCPUC Science Class 11

What Are the Dimensions of Volume of a Sphere of Radius A?

Advertisements
Advertisements

Question

What are the dimensions of volume of a sphere of radius a?

Short/Brief Note
Advertisements

Solution

Volume of a sphere of radius a, V =` 4/3 pi ( a )^3`
i.e [ V ] = L × L × L = L3

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Introduction to Physics - Short Answers [Page 8]

APPEARS IN

HC Verma Concepts of Physics Volume 1 and 2 [English]
Chapter 1 Introduction to Physics
Short Answers | Q 2.2 | Page 8

RELATED QUESTIONS

It is desirable that the standards of units be easily available, invariable, indestructible and easily reproducible. If we use foot of a person as a standard unit of length, which of the above features are present and which are not?


Suggest a way to measure the thickness of a sheet of paper.


Suppose a quantity x can be dimensionally represented in terms of M, L and T, that is, `[ x ] = M^a L^b T^c`.  The quantity mass


A dimensionless quantity


Find the dimensions of
(a) angular speed ω,
(b) angular acceleration α,
(c) torque τ and
(d) moment of interia I.
Some of the equations involving these quantities are \[\omega = \frac{\theta_2 - \theta_1}{t_2 - t_1}, \alpha = \frac{\omega_2 - \omega_1}{t_2 - t_1}, \tau = F . r \text{ and }I = m r^2\].
The symbols have standard meanings.


Find the dimensions of magnetic field B.
The relevant equation are \[F = qE, F = qvB, \text{ and }B = \frac{\mu_0 I}{2 \pi a};\]

where F is force, q is charge, v is speed, I is current, and a is distance.


Find the dimensions of magnetic permeability \[\mu_0\] 
The relevant equation are \[F = qE, F = qvB, \text{ and }B = \frac{\mu_0 I}{2 \pi a};\]

where F is force, q is charge, v is speed, I is current, and a is distance.


Test if the following equation is dimensionally correct:
\[V = \frac{\pi P r^4 t}{8 \eta l}\]

where v = frequency, P = pressure, η = coefficient of viscosity.


Let x and a stand for distance. Is
\[\int\frac{dx}{\sqrt{a^2 - x^2}} = \frac{1}{a} \sin^{- 1} \frac{a}{x}\] dimensionally correct?


Can a vector have zero component along a line and still have nonzero magnitude?


Is the vector sum of the unit vectors  \[\vec{i}\] and \[\vec{i}\] a unit vector? If no, can you multiply this sum by a scalar number to get a unit vector?

 


Which of the sets given below may represent the magnitudes of three vectors adding to zero?


A vector \[\vec{A}\] points vertically upward and \[\vec{B}\] points towards the north. The vector product \[\vec{A} \times \vec{B}\] is


The radius of a circle is stated as 2.12 cm. Its area should be written as


Let \[\vec{C} = \vec{A} + \vec{B}\]


Let the angle between two nonzero vectors \[\vec{A}\] and \[\vec{B}\] be 120° and its resultant be \[\vec{C}\].


Let \[\vec{a} = 4 \vec{i} + 3 \vec{j} \text { and } \vec{b} = 3 \vec{i} + 4 \vec{j}\]. Find the magnitudes of (a)  \[\vec{a}\] ,  (b)  \[\vec{b}\] ,(c) \[\vec{a} + \vec{b} \text { and }\] (d) \[\vec{a} - \vec{b}\].


Two vectors have magnitudes 2 unit and 4 unit respectively. What should be the angle between them if the magnitude of the resultant is (a) 1 unit, (b) 5 unit and (c) 7 unit.


Draw a graph from the following data. Draw tangents at x = 2, 4, 6 and 8. Find the slopes of these tangents. Verify that the curve draw is y = 2x2 and the slope of tangent is \[\tan \theta = \frac{dy}{dx} = 4x\] 
\[\begin{array}x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ y & 2 & 8 & 18 & 32 & 50 & 72 & 98 & 128 & 162 & 200\end{array}\]


If π = 3.14, then the value of π2 is ______


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×