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Units & Measurements

NEET Physics · 152 questions · Page 10 of 16 · Click an option or "Show Solution" to reveal answer

Q91
Which pair do NOT have equal dimensions?
A Energy and torque
B Force and impulse
C Angular momentum and Planck constant
D Elastic modulus and pressure
Correct Answer
Option B
Solution

Force=[MLT^{-2}], Impulse=[MLT^{-1}]. Different.

Q92
The dimension of dfrac12varepsilon0E2\\dfrac{1}{2}\\varepsilon_0 E^2 is:
A ML2T−2ML^2T^{-2}
B ML−1T−2ML^{-1}T^{-2}
C ML2T−1ML^2T^{-1}
D MLT−1MLT^{-1}
Correct Answer
Option B
Solution

Energy density = Energy/Volume = [ML−1T−2][ML^{-1}T^{-2}]

Q93
If dimensions of a physical quantity are MaLbTcM^a L^b T^c, physical quantity is:
A velocity if a=1,b=0,c=-1
B acceleration if a=1,b=1,c=-2
C force if a=0,b=-1,c=-2
D pressure if a=1,b=-1,c=-2
Correct Answer
Option D
Solution

Pressure = [ML−1T−2][ML^{-1}T^{-2}]: a=1,b=-1,c=-2

Q94
Which two of the following have the same dimensions? 1.Energy density 2.Refractive index 3.Dielectric constant 4.Young's modulus 5.Magnetic field
A 1 and 4
B 1 and 5
C 2 and 4
D 3 and 5
Correct Answer
Option A
Solution

Energy density = Young's modulus = [ML−1T−2][ML^{-1}T^{-2}]

Q95
If error in radius of sphere is 2%, error in volume is:
A 8%
B 2%
C 4%
D 6%
Correct Answer
Option D
Solution

V = (4/3)πR^3, dV/V = 3 dR/R = 3×2% = 6%

Q96
Dimensions of resistance in terms of M,L,T,I:
A [ML2T−2][ML^2T^{-2}]
B [ML2T−1I−1][ML^2T^{-1}I^{-1}]
C [ML2T−3I−2][ML^2T^{-3}I^{-2}]
D [ML2T−3I−1][ML^2T^{-3}I^{-1}]
Correct Answer
Option C
Solution

R=V/I, [V]=[ML^2T^{-3}I^{-1}], [R]=[ML2T−3I−2][ML^2T^{-3}I^{-2}]

Q97
If error in measurement of radius of sphere is 2%, error in determination of volume is:
A 8%
B 2%
C 4%
D 6%
Correct Answer
Option D
Solution

dV/V = 3dR/R = 6%

Q98
A student measures distance in free fall. Max % errors in distance and time are e1 and e2. % error in g is:
A e2-e1
B e1+2e2
C e1+e2
D e1-2e2
Correct Answer
Option B
Solution

g=2h/t^2, dg/g = dh/h + 2dt/t = e1+2e2

Q99
If force [F], acceleration [A], time [T] are fundamental, dimensions of energy are:
A [FA^{-1}T]
B [FAT]
C [FAT^2]
D [FAT^{-1}]
Correct Answer
Option C
Solution

E proportional to F.A.T^2 from dimensional analysis

Q100
The speed of light in vacuum is taken as unity. If light takes 6 min 40 s to reach the Earth from the Sun, the distance between the Sun and the Earth in new unit is:
A 3×1083 \times 10^8
B 500
C 3×10103 \times 10^{10}
D 400
Correct Answer
Option D
Solution

Time, t=6min⁡40 st=6 \min 40 \mathrm{~s}

=360+40=400 s\begin{aligned} & =360+40 \\ & =400 \mathrm{~s} \end{aligned}

Distance in new system d=vtd=v t

=1×400=400=1 \times 400=400
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