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

12th Grade > Physics

UNITS AND DIMENSIONS MCQs

Total Questions : 40 | Page 2 of 4 pages

Question 11. In C.G.S. system the magnitude of the force is 100 dynes. In another system where the fundamental physical quantities are kilogram, metre and minute, the magnitude of the force is

0.036
0.36
3.6
36

Discuss Question

Answer: Option C. -> 3.6
:
C

n_{2} = n_{1} {(\frac{M_{1}}{M_{2}})}^{1} {(\frac{L_{1}}{L_{2}})}^{1} {(\frac{T}{T_{2}})}^{- 2}

= 100 {(\frac{g m}{k g})}^{1} {(\frac{c m}{m})}^{1} {(\frac{s e c}{m i n})}^{- 2}

= 100 {(\frac{g m}{10^{3} g m})}^{1} {(\frac{c m}{10^{2} c m})}^{1} {(\frac{s e c}{60 s e c})}^{- 2}

n_{2} = \frac{3600}{10^{3}} = 3.6

Question 12. While measuring the acceleration due to gravity by a simple pendulum, a student makes a positive error of 1% in the length of the pendulum and a negative error of 3% in the value of time period. His percentage error in the measurement of g by the relation

g = 4 π^{2} (\frac{l}{T^{2}})

will be

Discuss Question

Answer: Option C. -> 7%
:
C
Percentage error in

g = (% e r r o r i n l) + 2 (% e r r o r i n T) = 1 % + 2 (3 %) = 7 %

Question 13. The position of a particle at time t is given by the relation x(t)=

(\frac{v_{0}}{α}) (1 - c^{- a t})

where

v_{0}

and

α

are constants . The dimensions of

v_{0}

and

α

are respectively

M0LT−1 and T−1
M0L1T0 and T−1
M0L1T−1 and LT−2
M0L1T−1 and T

Discuss Question

Answer: Option A. -> M0LT−1 and T−1
:
A
Dimension of

α

t =

[M^{0} L^{0} T^{0}] ∴ [α] = [T^{- 1}]

Again

[\frac{v_{0}}{α}]

= [L]so

[v_{0}] = [L T^{- 1}]

Question 14. The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate. If the maximum error in the measurement of force and length are respectively 4% and 2%, The maximum error in the measurement of pressure is

Discuss Question

Answer: Option D. -> 8%
:
D

P = \frac{F}{A} = \frac{F}{l^{2}},

So maximum error in pressure (P)

(\frac{Δ P}{P} \times 100)_{m a x} = \frac{Δ F}{F} \times 100 + 2 \frac{Δ l}{1} \times 100

= 4 % + 2 \times 2 % = 8 %

Question 15. From the dimensional consideration, which of the following equation is correct

T = 2π√R3GM
T =2π√GMR3
T =2π√GMR2
T =2π√R2GM

Discuss Question

Answer: Option A. -> T = 2π√R3GM
:
A
By substituting the dimension in T = 2

π \sqrt{\frac{R^{3}}{G M}}

we get

\sqrt{\frac{L^{3}}{M^{- 1} L^{3} T^{- 2} \times M}}

Question 16. If radius of the sphere is (5.3

\pm

0.1)cm. Then percentage error in its volume will be

3+6.01 ×1005.3
13× 0.01 ×1005.3
(3×0.15.3)×100
0.15.3×100

Discuss Question

Answer: Option C. -> (3×0.15.3)×100
:
C

Volume of sphere (v) =

\frac{4}{3} π γ^{3}

Percentage error in volume =3

\times \frac{Δ γ}{γ} \times

100 = (3

\times \frac{0.1}{5.3}) \times

100

Question 17. A small steel ball of radius

r

is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity

η

. After some time the velocity of the ball attains a constant value known as terminal velocity

v_{r}

. The terminal velocity depends on

(i)

the mass of the ball

m, (i i) η, (i i i) r a n d (i v)

acceleration due to gravity

g

. Which of the following relations is dimensionally correct

vT∝mgηr
vT∝ηrmg
vT∝ηrmg
vT∝mgrη

Discuss Question

Answer: Option A. -> vT∝mgηr
:
A
By substituting dimension of each quantity in R.H.S. of option (a) we get

[\frac{m g}{η r}] = [\frac{M \times L T^{- 2}}{M L^{- 1} T^{- 1} \times L}]

= [L T^{- 1}] .

This option gives the dimension of velocity.

Question 18. A force F is given by F=at +

b t^{2}

, where t is time. What are the dimensions of a and b

MLT−3 and ML2T−4
MLT−3 and MLT−4
MLT−1 and MLT0
MLT−4 and MLT−1

Discuss Question

Answer: Option B. -> MLT−3 and MLT−4
:
B
Dimension of a is same as that of

\frac{F}{t}

.i.e.

M L T^{- 3}

Dimension of b is same as that of

\frac{F}{t^{2}}

.i.e

M L T^{- 4}

Question 19. The unit of Stefan's constant

σ

Wm−2K−1
Wm2K−4
Wm−2K−4
Wm−2K4

Discuss Question

Answer: Option C. -> Wm−2K−4
:
C
Stefan's law is

E = σ (T^{4}) \Rightarrow σ = \frac{E}{T^{4}}

where,

E = \frac{E n e r g y}{A r e a \times T i m e} = \frac{W a t t}{m^{2}}

σ = \frac{W a t t - m^{- 2}}{K^{4}} = W a t t = m^{- 2} K^{- 4}

Question 20. Two quantities A and B have different dimensions. Which mathematical operation given below is physically meaningful

AB
A+B
A−B
can be A and B

Discuss Question

Answer: Option A. -> AB
:
A
Quantities having different dimensions can only be divided or multiplied but they cannot be added or subtracted.

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