If we did all things we are capable of, we would literally astound ourselves.

– Thomas A. Edison

Wednesday, December 23, 2009

Multiple Choice Questions on Dimensions of Physical Quantities

The world is a dangerous place, not because of those who 
do evil, but because of those who look on and do nothing. 
–Albert Einstein 

Today we will discuss a few questions on units and dimensions:

(1) Van der Waals equation of state for real gases is [P + (a/V2)](Vb) = RT where P is the pressure, V is the volume of one mole of gas, R is the universal gas constant, T is the temperature and a and b are constants. The dimensional formula of a is
(a) [M0L6T0]
(b) [ML–1T–2]
(c) [ML5T–2]
(d) [ML–2T–2]
(e) [ML3T–2]
This is a question popular among question setters and has appeared many times in various entrance test papers. Since a/V2 appears as added to P, the dimensions of a/V2 must be the same as those of P. Therefore, ‘a’ has the dimensions of PV2.
Note that pressure P is force per unit ares and hence the dimensional formula for P is [ML–1T–2]. The dimensional formula for V2 is [L6]. Therefore, the dimensional formula for ‘a’ is [ML5T–2].
(2) The dimensional formula for Stefan’s constant is
(a) [MT–3K–4]
(b) [ML2T–2K–4]
(c) [ML2T–2]
(d) [MT–2L0]
(e) [MT4L0]

This question appeared in Kerala Engineering Entrance (KEAM) 2009 question paper. You will find similar questions in other entrance test papers also.

We have E = σT4 where E is the energy radiated per second from unit area, σ is Stefan’s constant and T is the temperature of the black body.
Therefore, σ = E/T4
Note that energy has dimensional formula [ML2T–2]. Sine E is the energy radiated per second from unit area, the dimensional formula for E is [MT–3].
Therefore, the dimensional formula for Stefan’s constant σ is [MT–3K–4].
(3) Pick out the correct dimensions in length of the quantity μ0ε0 from the following:
(a) 2
(b) 1
(c) 1
(d) 2
(e) zero
You know that the speed ‘c of electromagnetic waves in free space is given by
c = 1/√(μ0ε0)
Therefore μ0ε0 = 1/c2 and the dimensional formula for μ0ε0 is [L–2T2]. The quantity μ0ε0 therefore has – 2 dimensions in length [Option (d)].
(4) Which of the following is dimensionless?
(a) Stress
(b) Gas constant
(c) Frequency of sound
(d) Efficiency of heat engine
(e) Thermal conductivity
The correct option is (d) since the efficiency is the ratio of the output power to the input power.

Saturday, December 05, 2009

Applications invited for Kerala Entrance Examinations for Admission to Medical/ Agriculture/ Veterinary/ Engineering/ Architecture Degree Courses 2010 (KEAM 2010)

The Commissioner for Entrance Examinations, Govt. of Kerala, has invited applications for the Entrance Examinations for admission to the following Degree Courses in various Professional Colleges in Kerala for 2010-2011.
(a) Medical (i) MBBS (ii) BDS (iii) BHMS (iv) BAMS (v) BSMS
(b) Agriculture (i) BSc. Hons. (Agriculture) (ii) BFSc. (Fisheries) (iii) BSc. Hons. (Forestry)
(c) Veterinary BVSc. & AH
(d) Engineering B.Tech. [including B.Tech. (Agricultural Engg.)/B.Tech. (Dairy Sc. & Tech.) courses under the Kerala Agricultural University]
(e) Architecture B.Arch.
[Candidates aspiring for B.Arch. course should also submit their application to the CEE. Even though there is no state level Entrance Examination for this purpose, these candidates should write the National Aptitude Test for Architecture and should forward the NATA score and mark list of the qualifying examination to the CEE on or before 05.06.2010].

Dates of Exam:
Engineering Entrance Examination (For Engineering courses except Architecture)
19.04.2010 Monday 10.00 A.M. to 12.30 P.M. Paper-I : Physics & Chemistry.
20.04.2010 Tuesday 10.00 A.M. to 12.30 P.M. Paper-II: Mathematics.

Medical Entrance Examination (For Medical, Agriculture and Veterinary Courses)
21.04.2010 Wednesday 10.00 A.M. to 12.30 P.M. Paper-I : Chemistry & Physics.
22-04.2010 Thursday 10.00 A.M. to 12.30 P.M. Paper-II: Biology.

Sale of Application Form through selected post offices: From  07-12-2009 to 06-01-2010
To see the list of selected post offices, visit http://www.cee-kerala.org/
Last Date for Receipt of Application by CEE: 06-01-2010 (Wednesday), before 5 P.M.

Facility for online submission of application in the case of non-reservation category and Non-Keralite category is available.

In addition to the multiple choice questions (of the type expected to appear in KEAM 2010) on this site, you will find many similar useful questions with solution at the site  http://physicsplus.blogspot.com.  If you want to see earlier KEAM questions only, type in ‘Kerala’ in the search box at the top left of this page and click on the search button or press the enter key.