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Units & Measurements

NEET Physics · 152 questions · Page 9 of 16 · Click an option or "Show Solution" to reveal answer

Q81
If dimensions of critical velocity are [etaxrhoyrz][\\eta^x \\rho^y r^z], where eta\\eta=viscosity, rho\\rho=density, r=radius, then x,y,z are:
A -1,-1,-1
B 1,1,1
C 1,-1,-1
D -1,-1,1
Correct Answer
Option C
Solution

From dimensional analysis: x=1, y=-1, z=-1

Q82
If energy (E), velocity (V) and time (T) are fundamental, surface tension dimensions are:
A [EV−2T−2][EV^{-2}T^{-2}]
B [E−2V−1T−3][E^{-2}V^{-1}T^{-3}]
C [EV−2T−1][EV^{-2}T^{-1}]
D [EV−1T−2][EV^{-1}T^{-2}]
Correct Answer
Option A
Solution

a=1, b=-2, c=-2. Surface tension = [EV−2T−2][EV^{-2}T^{-2}]

Q83
If force (F), velocity (V), time (T) are fundamental, dimensions of mass are:
A [FVT−1][FVT^{-1}]
B [FVT−2][FVT^{-2}]
C [FV−1T−1][FV^{-1}T^{-1}]
D [FV−1T][FV^{-1}T]
Correct Answer
Option D
Solution

From dimensional analysis: a=1, b=-1, c=1. Mass = [FV−1T][FV^{-1}T]

Q84
The pair of quantities having same dimensions is:
A Impulse and Surface Tension
B Angular momentum and Work
C Work and Torque
D Young's modulus and Energy
Correct Answer
Option C
Solution

Work = Torque = [ML2T−2][ML^2T^{-2}]

Q85
Percentage error in P = a3b2/(cd)a^3 b^2/(cd) where errors are 1%,2%,3%,4% is:
A 7%
B 4%
C 14%
D 10%
Correct Answer
Option C
Solution

3(1)+2(2)+3+4=14%

Q86
The velocity v of a particle is given by v=at+b/(t+c)v=at + b/(t+c). Dimensions of a, b, c are:
A [L],[LT],[LT^{-2}]
B [LT^{-2}],[L],[T]
C [L^2],[T],[LT^{-2}]
D [LT^{-2}],[LT],[L]
Correct Answer
Option B
Solution

a=[LT^{-2}], c=[T], b=[L]

Q87
The ratio of dimensions of Planck's constant to moment of inertia has dimensions of:
A time
B frequency
C angular momentum
D velocity
Correct Answer
Option B
Solution

h/I = [ML^2T^{-1}]/[ML^2] = [T^{-1}] = frequency

Q88
The unit of permittivity of free space varepsilon0\\varepsilon_0 is:
A coulomb/newton-metre
B newton-metre^2/coulomb^2
C coulomb^2/newton-metre^2
D coulomb^2/(newton-metre)^2
Correct Answer
Option C
Solution

From F=q2/(4pivarepsilon0r2)F = q^2/(4\\pi\\varepsilon_0 r^2), varepsilon0=q2/(4piFr2)\\varepsilon_0 = q^2/(4\\pi F r^2)

Q89
The dimensions of universal gravitational constant are:
A [M−1L3T−2][M^{-1}L^3T^{-2}]
B [ML2T−1][ML^2T^{-1}]
C [M−2L3T−2][M^{-2}L^3T^{-2}]
D [M−2L2T−1][M^{-2}L^2T^{-1}]
Correct Answer
Option A
Solution

From F=Gm1m2/r2F = Gm_1 m_2/r^2: G = [M−1L3T−2][M^{-1}L^3T^{-2}]

Q90
The dimensions of Planck's constant equal that of:
A energy
B momentum
C angular momentum
D power
Correct Answer
Option C
Solution

h = [ML2T−1][ML^2T^{-1}] = angular momentum

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