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Units, Dimension And Measurement Mcq
Quiz 7
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Q.1
The mass M of stone is flowing river depends on the speed v of a water, its density ρ and gravitational acceleration g. Then with the help of dimensional analysis, the mas of stone is ... times proportional to the power of the speed of water.... .... [ Guj T.B.]
0%
a) 2
0%
b) 3
0%
c) 6
0%
d) 8
Explanation
m = va ρb gc M1 = [LaT-a] [MbL-3b][LcT-2c] Comparing indices on both side we get 1 = b 0 = a-3b+c 0 = -a-2c On simplifying above equations we get a = 6, b = 1, c =-3 correct answer is (c) Answer : (c)
Q.2
The observation in experiment, length of rod are 2.51m, 2.56m, 2.49m then percentage error in length is ... ... [ Guj T.B.]
0%
a) 0.1%
0%
b) 1%
0%
c) 10%
0%
d) 0.01%
Explanation
Average reading = (2.51+2.56+2.49)/3 = 2.52 m Absoulte error of each observation Δl1 = 2.52 -2.51 = 0.01 Δl2 = 2.52 -2.56 = -0.04 Δl2 = 2.52 -2.49 = 0.03 Average absolute error, considering only magnitude Average absolute error = (0.01 + 0.04 + 0.03)/3 = 0.03 m Length of rod = (2.52 ±0.03) m Relative error = Absolute error/ average value = 0.03/2.52 = 0.01 Percentage error = Relative error ×100 Percentage error = 0.01 ×100 = 1% Answer : (b)
Q.3
If F = a√x + bt2 formula is dimensionally valid then what is the dimensional formula for 'a', here F= force and x = distance, t = time) ... .... [ Guj T.B.]
0%
a) M1L1T-1
0%
b) M1L1/2 T-2
0%
c) M1L1T-2
0%
d) M0L-1/2T2
Explanation
Use dimensional analysis Answer : (b)
Q.4
The periodic time T of the satellite revolving around the planet on circular orbit depends on a mass m, radius r and universal gravitational constant G, then T2 ∝ ... .. [ Guj T.B.]
0%
a) r1/2
0%
b) r3/2
0%
c) r
0%
d) r3
Explanation
T =k ma rb Gc Let k be dimensionless constant Dimension of LHS = RHS T1 = [Ma][Lb][M-cL3cT-2c] Comparing indices of MLT we get a = c = -1/2, b = 3/2 Thus T ∝ l3/2 T2 ∝ r3 Answer : (d)
Q.5
The formula for a physical quantity is here x, y,z are length . this physical quantity is ... ... [ Guj T.B. ]
0%
a) velocity
0%
b) length
0%
c) area
0%
d) volume
Explanation
Answer : (d)
Q.6
If E, M, L and G are energy, mass, angular momentum nad gravitational constnat respectively the dimensional formula of following equation will be ... ... [ Guj T.B]
0%
a) time
0%
b) angle
0%
c) mass
0%
d) length
Explanation
Dimensional formula for Energy = [M1 Angular momentum L = mvr = [M1L2T-1] gravitational constant G = [ M-1L3T-2 ] Mass =M = M1 Substitute dimensional formula in equation and solve, we get dimensions zero Now only angle do not have any dimension from given option thus angle is correct Answer : (b)
Q.7
If velocity of light is C, gravitational acceleration g and pressure P taken as fundamental unit then gravitational constant is ... .... [ Guj T.B. ]
0%
a) C0gP-3
0%
b) C2g3p-2
0%
c) C0g2P-1
0%
d) C2g2P-3
Explanation
Let G = CxgyPz Dimensions of G = [ M1L3L-2 dimension of g = [ L1T-2 Dimension pf P = [M1L-1T-2 Now substitute dimensions of G, g and P and solve equations for x , y and z x = 0, y=2, z = -1 Correct option is Answer : (c)
Q.8
A ground has length (100 ± 5) m and breadth (50 ± 4) m, then area of ground is ...m2 .... ... [ Guj T.B.]
0%
a)(5000 ± 650)
0%
b) ( 500 ± 65 )
0%
c) (5000 ± 600 )
0%
d) (500 ± 650)
Explanation
Area = l ×b A = 100× 50 = 5000 m3 Answer : (a)
Q.9
To make mixed metal, the mass of gold is 1.45g, silver is 2.613 g, copper is 2.8 g and zinc is 1.79g. the mass of mixed metal is ... in terms of significant figure ... ... [ Guj T.B.]
0%
a) 8.5
0%
b) 8.6
0%
c) 8.7
0%
d) 8.9
Explanation
Answer : (c)
Q.10
1 radian = ... ..
0%
a)
0%
b)
0%
c)
0%
d)
Explanation
Answer : (b)
Q.11
Rounding off 9637 up to two digit, we get
0%
a) 9600
0%
b) 9630
0%
c) 9640
0%
d) 9700
Explanation
Answer : (a)
Q.12
Number of significant figure in 0.00230 is ....
0%
a) 5
0%
b) 3
0%
c) 4
0%
d) None
Explanation
Answer : (b)
Q.13
A sphere has radius r with area A = 4πr2 then waht will be the equation of relative error ΔA/A ?
0%
a)
0%
b)
0%
c)
0%
d)
Explanation
Answer : (b)
Q.14
What is the weight of particle having mass 100 grams?
0%
a) 9.8 N
0%
b) 9.8 × 104N
0%
c) 9.8 ×104 dyne
0%
d) 980 dyne
Explanation
100 g × 980 = 9.8×104 dyne Answer : (b)
Q.15
If the force F is represented by equation F = Pt-1 + Qt then unit of P is same as that of .... (t=time)
0%
a) acceleration
0%
b) velocity
0%
c) displacement
0%
d) momentum
Explanation
Answer : (d)
Q.16
Dimensional formula for angular velocity is ... ...
0%
a) M0L0T1
0%
b) M0L1T-1
0%
c) M0L0T-1
0%
d) M0L0T-2
Explanation
Angular velocity ω = 2π/T Answer : (c)
Q.17
Wave length of visible light is 0.00006 m then it is =...
0%
a) 6 microm
0%
b) 60 micron
0%
c) 600 micron
0%
d) 0.6 micron
Explanation
Wave length = 0.00006 m = 6×10-5 = 60×10-6 m = 60 micron Answer : (b)
Q.18
In series connection of resistance Rs = R1+R2 then what is the equation of relative error ....
0%
a)
0%
b)
0%
c)
0%
d)
Explanation
Rs = R1 + R2 .... eq(1) ΔRs = ΔR1 + ΔR2 ... ..eq(2) dividing eq(2) by eq(1) we get option "c" Answer : (c)
Q.19
For resistance R = V/I, V = 100 ± 5 volts and I = 10 ±0.02 ampere, then calculate percentage error in resistance R
0%
a) 5%
0%
b) 7%
0%
c) 5.2%
0%
d) 2.5%
Explanation
Use relative error formula and then multiply by 100 Relative error formula Answer : (c)
Q.20
The percentage error in 125.0±0.5cm is ....
0%
a) 4%
0%
b) 0.04%
0%
c) 0.4%
0%
d) 40%
Explanation
Answer : (c)
Q.21
Equation of displacement is x = at + bt2 where x is distnce in kilometer and time t in seconds then unot of b is
0%
a) km/s
0%
b) km-s
0%
c) km/s2
0%
d) km -s2
Explanation
Answer : (c)
Q.22
'a' is the acceleration of an object in equation x = Kamtn where t is time, then calculate the value of m and n.
0%
a) m = 1, n = 1
0%
b) m = 1, n = 2
0%
c) m = 2, n = 1
0%
d) m =2, n = 2
Explanation
Answer : (b)
Q.23
For parallel connection of resistors equivalent resistance is given by following equation then which of the following equation is true
0%
a)
0%
b)
0%
c)
0%
d)
Explanation
Answer : (b)
Q.24
Percentgae error in mass and length are 0.26% nad 0.38% respectively then what is the percentage error in density? [ guj T.B.]
0%
a) 14%
0%
b) 1.4%
0%
c) 1.04%
0%
d) 1.44%
Explanation
Answer : (b)
Q.25
S = A(1 -e-Bxt), where S = speed, x = displacement t = times then unit of B is ...
0%
a) m-1 s-1
0%
b) m-2 s
0%
c) s-2
0%
d) s-1
Explanation
Same unit can be added and subtracted. Since 1 have no unit e-Bxt do not have unit or Bxt is unit less Thus unit of B = 1/xt = 1/ms =m- s-1 Answer : (a)
Q.26
Match the following
1) joule
a) henry ×ampere/sec
2) watt
b) farady ×volt
3) volt
c) cooumb × volt
4) coloumb
d) orestad × cm
- -
e) ampere × gauss
- -
f) (ampere)
2
× ohm
0%
a) 1 -a, 2 -f, 3 -e, 4 -d
0%
b) 1 -c, 2 -f, 3 -a, 4 -e
0%
c) 1 -c, 2 -f, 3 -a, 4 -b
0%
d) 1 -b, 2 -f, 3 -a, 4 -c
Explanation
Answer : (c)
Q.27
Match the following ...
I
II
a) distance between earth and star
1) Micron
b) inter molecular distance in solids
2) Angstrom
c) dimensions of molecule
3) light year
d) wave length of infrared rays
4) fermi
- -
5) kilometer
0%
a) a -5, b-4, c -2, d -1
0%
b) a -3, b -2, c -4, d -1
0%
c) a -5, b -2, c -4, d -3
0%
d) a -3, b-4, c -1, d -2
Explanation
Answer : (b)
Q.28
Match the following
a) angular momentum
1) M
1
L
2
T
-2
b) latent heat
2) M
1
L
2
Q
-2
c) torque
3) M
1
L
2
T
-1
d) tcapacitance
4) M
1
L
3
T
-1
Q
-2
e) inductance
5) M
-1
L
-2
T
2
Q
2
f) resistance
6) M
0
L
2
T
-2
0%
a) a -3, b -6, c -1, d -5, e -2, f -4
0%
b) a -3, b -6, c -5, d -2, e -4, f -1
0%
c) a -3, b -5, c -2, d -4, e -21, f -6
0%
d) a -6, b -5, c -2, d -4, e -1, f -3
Explanation
Answer : (a)
Q.29
Assertion: Method of dimensions cannot be used for deriving formula containing trigonometric ratios Reason: This is because trigonometric ratios have no dimensions
0%
a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion
0%
b) The Assertion and Reason are true but Reason is not correct explanation of Assertion
0%
c) Assertion is true but, Reason is false
0%
d) Assertion is false but, Reason is true
Explanation
Answer : (a)
Q.30
Assertion: In the following , m is linear mass density Reason" Linear mass density = mass/ volume
0%
a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion
0%
b) The Assertion and Reason are true but Reason is not correct explanation of Assertion
0%
c) Assertion is true but, Reason is false
0%
d) Assertion is false but, Reason is true
Explanation
Answer : (b)
0 h : 0 m : 1 s
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