Important Questions On Units And Dimensions..

check the correctness of the relation dimensionally:

S(n)=u+1/2a(2n-1)

Subtract 0.2 kg from 34 kg with due regard to significant figures.

by what % should the pressure of a given mass of a gas be increased so as to decrease its volume by 10% at a constant temperature ?

the least count of the length of a cylinder is 0.1cm. the least count of its diameter is 0.01 cm. the measurement of length is 5.0 cm and radius is 2.0 cm . what is the % error in volume ??

specific resistance can be represented dimensionally in terms of charge Q as -------ans is ML^-3T^-1Q^-2 ( plsss explain)

sir,does the least count gets halved when we divide diameter by 2 to get radius ??

if g be acceleration due to gravity and K be rotational kinetic energy of the earth .suppose the earth's radius decreases by 2%.keeping all other quantities constant,--

a) g increases by 2% and k increases by 2%

b) g increases by 4% and k increases by 4%

c) g decreases by 4% and k decreases by 2%

d) g decreases by 2% and k decreases by 4%

a planet of mass m rotates around a star of mass M. the time period of revolution is T while the average distance of the planet from the star is a. it is known tht there exists a relationship between them.find it.assume the dimensional expression for G.

11 Answers

11
Anirudh Narayanan ·

I
Does the 1st expression represent displacement in nth second?

II
isn't it 33.8 ? 33.8000 if you like ;)

III

P= k/V

P'=k/0.9V

P/P'= 0.9

P'=P/0.9 and get %age increase :)
Contd...

11
Anirudh Narayanan ·

Contd.....

ρ = RA/L
= VA/IL
Substituting units,
= kgms-2m.m2s/C2m
= kg m3 C-2 s-1

No. Least count is same. Why do you ask?

Well, that's all I could manage. Sorry. ;)

1
varun ·

I - 1st - dimensionally incorrect

II - 34 Kg

III - 100/9 %

IV -

V - s = RA/L

= (V/I)(A/L)

= (W/Q)/(Q/t)(L2/L)

=(kg m2 s-2 s m) / (Q2)

=ML3T-1Q-2

VI - No

VII -

1
varun ·

IV - 5.0 ± 0.1 and 2.00 ± 0.01

Therefore % error is

(.1 / 5 ) * 100 + (.01/2)*100

=2 + .5%

=2.5%

11
Anirudh Narayanan ·

Hey, pati. Does the 1st expression represent displacement in nth second?

1
varun ·

yes but here he gave

S(n)=u+1/2a(2n-1)

S and u are not of same dimensions .. it must have been u(1s)

11
Anirudh Narayanan ·

It IS u(1s). So dimensionally correct. :)

1
skygirl ·

the first one is dimensionally correct only..
actual the time=1s is not written in the equation dtas y it seems that it is incorrect but actually not so...

1
skygirl ·

for second one, ans =30kg.
(since no. of significant fig in 0.2 are one)

1
skygirl ·

for that least count question,
least count is measuerd for an instrument NOT for the thing we are measuring... (it is the least possible measurement done by that instrument.. for ex., least count of a simple ruler is 1mm.. it will remain same whether u measure diameter or radius or himalaya or nething for dat matter with it ...)

1
greatvishal swami ·

1. i think we have to solve the Qs using info provided
clerly its incorrect

2. 34Kg final result should retain as many deci places as in num with least deci places
& from where dat 30 came sky

3. P proportional 1/V
diffrentiate to get ΔP=-Δv so 10 percent inc

last g prop 1/r2
diff Δg=-2Δr so 4 % inc

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