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


India has had a long and unbroken tradition of great scholarship — in mathematics, astronomy, linguistics, logic and ethics. Yet, in parallel with this, several superstitious and obscurantistic attitudes and practices flourished in our society and unfortunately continue even today — among many educated people too. How will you use your knowledge of science to develop strategies to counter these attitudes ?


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


If all the terms in an equation have same units, is it necessary that they have same dimensions? If all the terms in an equation have same dimensions, is it necessary that they have same units?


Choose the correct statements(s):


Choose the correct statements(s):
(a) All quantities may be represented dimensionally in terms of the base quantities.
(b) A base quantity cannot be represented dimensionally in terms of the rest of the base quantities.
(c) The dimensions of a base quantity in other base quantities is always zero.
(d) The dimension of a derived quantity is never zero in any base quantity.


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.


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.


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


If \[\vec{A} \times \vec{B} = 0\] can you say that

(a) \[\vec{A} = \vec{B} ,\]

(b) \[\vec{A} \neq \vec{B}\] ?


Let \[\vec{A} = 5 \vec{i} - 4 \vec{j} \text { and } \vec{B} = - 7 \cdot 5 \vec{i} + 6 \vec{j}\]. Do we have \[\vec{B} = k \vec{A}\] ? Can we say \[\frac{\vec{B}}{\vec{A}}\] = k ?


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.


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) \[\vec{a} - \vec{b}\].


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.


A carrom board (4 ft × 4 ft square) has the queen at the centre. The queen, hit by the striker moves to the from edge, rebounds and goes in the hole behind the striking line. Find the magnitude of displacement of the queen (a) from the centre to the front edge, (b) from the front edge to the hole and (c) from the centre to the hole.


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


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


Give an example for which \[\vec{A} \cdot \vec{B} = \vec{C} \cdot \vec{B} \text{ but } \vec{A} \neq \vec{C}\].


Round the following numbers to 2 significant digits.
(a) 3472, (b) 84.16. (c)2.55 and (d) 28.5


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×