Units And Dimensions(12th Grade > Physics ) Questions and answers for exam Preparation

12th Grade > Physics

UNITS AND DIMENSIONS MCQs

Total Questions : 40 | Page 3 of 4 pages

Question 21. Select the pair whose dimensions are same

Pressure and stress
Stress and strain
Pressure and force
Power and force

Discuss Question

Answer: Option A. -> Pressure and stress
:
A
Pressure

= \frac{F o r c e}{A r e a} = M L^{- 1} T^{- 2}

Stress

= \frac{R e s t o r i n g f o r c e}{A r e a} = M L^{- 1} T^{- 2}

Question 22. A dimensionally consistent relation for the volume V of a liquid of coefficient of viscosity

η

flowing per second through a tube of radius r and length l and having a pressure difference P across its end, is

V=πPγ48ηl
V=πηl8Pγ4
V=8Pηlπγ4
V = πPη8lγ4

Discuss Question

Answer: Option A. -> V=πPγ48ηl
:
A
Formula for viscosity

η = \frac{π P γ^{4}}{8 V l} \Rightarrow

V =

\frac{π P γ^{4}}{8 η l}

Question 23. The velocity v (in cm / sec) of a particle is given in terms of time t(in sec) by the relation v =

α

t +

\frac{b}{t + c}

; the dimensions of a, b and c are

a = L2, b = T, c = LT2
a = LT2, b = LT, c = L
a = LT−2, b = L, c = T
a = L, b = LT, c = T2

Discuss Question

Answer: Option C. -> a = LT−2, b = L, c = T
:
C
From the principle of dimensional homogeneity [v] =

[α t] \Rightarrow [α] = [L T^{- 2}]

. similarly [b] = [L]and [c] = [T]

Question 24. If velocity v, acceleration A and force B are chosen as fundamental quantities, then the dimensional formula of angular momentum in terms of v, A and F would be

FA−1v
Fv3A−2
Fv2A−1
F2v2A−1

Discuss Question

Answer: Option B. -> Fv3A−2
:
B
L

\propto v^{x} A^{y} F^{z} \Rightarrow

L =

k v^{x} A^{y} F^{z}

Putting the dimenstions in the above relation

[M L^{2} T^{- 1}] = k [L T^{- 1}]^{x} [L T^{- 2}]^{y} [M L T^{- 2}]^{z}

\Rightarrow [M L^{2} T^{- 1}] = k [M^{z} L^{x + y + z} T^{- x - 2 y - 2 z}]

Comparing the pwers of M,LandT
z=1 ...(i)
x+y+z =2...(ii)
-x-2y-2z =-1 ...(iii)
On solving (i),(ii), and (iii) x=3, y=-2 ,z=1
So dimension of L in terms of v,Aandf
[L] =

[F v^{3} A^{- 2}]

Question 25. If P represents radiation pressure, c represents speed of light and Q represents radiation energy striking a unit area per second, then non-zero integers x,y and z such that

P^{x} Q^{y} C^{z}

is dimensionless, are

x=1,y=1,z=-1
x=1,y=-1,z=1
x=-1,y=1,z=1
x=1,y=1,z=1

Discuss Question

Answer: Option B. -> x=1,y=-1,z=1
:
B
By substituting the dimension of given quantities

[M L^{- 1} T^{- 2}]^{x} [M T^{- 3}]^{y} [L T^{- 1}]^{z} = [M L T]^{0}

By comparing the power of M,L,Tin both sides x + y = 0 .....(i)
-x + z = 0 ......(ii)
-2x - 3y - z = 0 ......(iii)
The only values of x,y,zsatisfying ((i),(ii)and (iii)corresponds to (b).

Question 26. Two quantities A and B have different dimensions. Which mathematical operation given below is physically meaningful?