English
Karnataka Board PUCPUC Science Class 11

What Are the Dimensions of the Ratio of the Volume of a Cube of Edge A To the Volume of a Sphere of Radius A?

Advertisements
Advertisements

Question

What are the dimensions of the ratio of the volume of a cube of edge a to the volume of a sphere of radius a?

Short/Brief Note
Advertisements

Solution

The ratio of the volume of the cube to the volume of the sphere is a dimensionless quantity.

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 2.3 | Page 8

RELATED QUESTIONS

Some of the most profound statements on the nature of science have come from Albert Einstein, one of the greatest scientists of all time. What do you think did Einstein mean when he said : “The most incomprehensible thing about the world is that it is comprehensible”?


What are the dimensions of volume of a cube of edge a.


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


If two quantities have same dimensions, do they represent same physical content?


Find the dimensions of frequency .


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 the specific heat capacity c.
(a) the specific heat capacity c,
(b) the coefficient of linear expansion α and
(c) the gas constant R.
Some of the equations involving these quantities are \[Q = mc\left( T_2 - T_1 \right), l_t = l_0 \left[ 1 + \alpha\left( T_2 - T_1 \right) \right]\] and PV = nRT.


Is it possible to add two vectors of unequal magnitudes and get zero? Is it possible to add three vectors of equal magnitudes and get zero?


Can you add two vectors representing physical quantities having different dimensions? Can you multiply two vectors representing physical quantities having different dimensions?


Let ε1 and ε2 be the angles made by  \[\vec{A}\] and -\[\vec{A}\] with the positive X-axis. Show that tan ε1 = tan ε2. Thus, giving tan ε does not uniquely determine the direction of \[\vec{A}\].

  

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


The magnitude of the vector product of two vectors \[\left| \vec{A} \right|\] and \[\left| \vec{B} \right|\] may be

(a) greater than AB
(b) equal to AB
(c) less than AB
(d) equal to zero.


A vector \[\vec{A}\] makes an angle of 20° and \[\vec{B}\] makes an angle of 110° with the X-axis. The magnitudes of these vectors are 3 m and 4 m respectively. Find the resultant.


A spy report about a suspected car reads as follows. "The car moved 2.00 km towards east, made a perpendicular left turn, ran for 500 m, made a perpendicular right turn, ran for 4.00 km and stopped". Find the displacement of the car.


Prove that \[\vec{A} . \left( \vec{A} \times \vec{B} \right) = 0\].


If  \[\vec{A} = 2 \vec{i} + 3 \vec{j} + 4 \vec{k} \text { and } \vec{B} = 4 \vec{i} + 3 \vec{j} + 2 \vec{k}\] find \[\vec{A} \times \vec{B}\].


A curve is represented by y = sin x. If x is changed from \[\frac{\pi}{3}\text{ to }\frac{\pi}{3} + \frac{\pi}{100}\] , find approximately the change in y. 


Write the number of significant digits in (a) 1001, (b) 100.1, (c) 100.10, (d) 0.001001.


In a submarine equipped with sonar, the time delay between the generation of a pulse and its echo after reflection from an enemy submarine is observed to be 80 s. If the speed of sound in water is 1460 ms-1. What is the distance of an enemy submarine? 


Jupiter is at a distance of 824.7 million km from the Earth. Its angular diameter is measured to be 35.72˝. Calculate the diameter of Jupiter.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×