English
Karnataka Board PUCPUC Science Class 11

Suppose a Quantity X Can Be Dimensionally Represented in Terms of M, L and T, that Is, `[ X ] = M^A L^B T

Advertisements
Advertisements

Question

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

Options

  • can always be dimensionally represented in terms of L, T and x,

  • can never be dimensionally represented in terms of L, T and x,

  • may be represented in terms of L, T and x if a = 0,

  • may be represented in terms of L, T and x if a ≠ 0

MCQ
Advertisements

Solution

may be represented in terms of L, T and x if a ≠ 0
If a = 0, then we cannot represent mass dimensionally in terms of L, T and x, otherwise it can be represented in terms of L, T and x.

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Introduction to Physics - MCQ [Page 9]

APPEARS IN

HC Verma Concepts of Physics Volume 1 and 2 [English]
Chapter 1 Introduction to Physics
MCQ | Q 3 | Page 9

RELATED QUESTIONS

“Every great physical theory starts as a heresy and ends as a dogma”. Give some examples from the history of science of the validity of this incisive remark


“It is more important to have beauty in the equations of physics than to have them agree with experiments”. The great British physicist P. A. M. Dirac held this view. Criticize this statement. Look out for some equations and results in this book which strike you as beautiful.


A unitless quantity


Find the dimensions of pressure.


The height of mercury column in a barometer in a Calcutta laboratory was recorded to be 75 cm. Calculate this pressure in SI and CGS units using the following data : Specific gravity of mercury = \[13 \cdot 6\] , Density of \[\text{ water} = {10}^3 kg/ m^3 , g = 9 \cdot 8 m/ s^2\] at Calcutta. Pressure
= hpg in usual symbols.


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.


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


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 \[\vec{A}\].

  

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?

 


Let \[\vec{A} = 3 \vec{i} + 4 \vec{j}\]. Write a vector \[\vec{B}\] such that \[\vec{A} \neq \vec{B}\], but A = B.


A situation may be described by using different sets coordinate axes having different orientation. Which the following do not depended on the orientation of the axis?
(a) the value of a scalar
(b) component of a vector
(c) a vector
(d) the magnitude of a vector.


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.


Add vectors \[\vec{A} , \vec{B} \text { and } \vec{C}\]  each having magnitude of 100 unit and inclined to the X-axis at angles 45°, 135° and 315° respectively.


Refer to figure (2 − E1). Find (a) the magnitude, (b) x and y component and (c) the angle with the X-axis of the resultant of \[\overrightarrow{OA}, \overrightarrow{BC} \text { and } \overrightarrow{DE}\].


Suppose \[\vec{a}\] is a vector of magnitude 4.5 units due north. What is the vector (a) \[3 \vec{a}\], (b) \[- 4 \vec{a}\] ?


Let \[\vec{a} = 2 \vec{i} + 3 \vec{j} + 4 \vec{k} \text { and } \vec{b} = 3 \vec{i} + 4 \vec{j} + 5 \vec{k}\] Find the angle between them.


The electric current in a charging R−C circuit is given by i = i0 e−t/RC where i0, R and C are constant parameters of the circuit and t is time. Find the rate of change of current at (a) t = 0, (b) t = RC, (c) t = 10 RC.


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×