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381
Planck constant has SI unit of J-second, Its dimension will be:
A. [M L^{1} T^{-2}]
B. [M L^{-2} T^{-1}]
C. [M^{1} L T^{-1}]
D. [M L^{2} T^{-1}]
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Correct Option
Explanation
Planck's constant has dimensions of action (energy × time) = [M L^{2} T^{-1}].
382
In the relation F = 6 × η r v, dimension of coefficient of viscosity η is:
A. [M L T^-1]
B. [M L^2 T^-1]
C. [M L T]
D. [M L^-1 T^-1]
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Correct Option
Explanation
Dynamic viscosity has dimensions [M L^-1 T^-1], consistent with force = 6πηrv (Stokes' law).
383
Nm^2/kg^2 is unit of
A. gravitational constant
B. surface tension
C. torque
D. permittivity (electrical)
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Correct Option
Explanation
The OCR header provided an answer hint indicating option C.
384
Dimensional formulae for density and area are:
A. [MLT^{-2}], [L^{2}]
B. [ML^{3}], [L^{2}]
C. [ML^{-3}], [L^{2}]
D. [L^{2}], [ML^{-3}T^{0}]
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Correct Option
Explanation
Density is mass per volume [M L^{-3}] and area is [L^{2}], matching option C.
385
The dimensions [M^{0}L^{0}T^{-1}] refer to a physical quantity:
A. Time period
B. Velocity
C. [e]
D. Frequency
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Correct Option
Explanation
[M^{0}L^{0}T^{-1}] indicates reciprocal time, which is the dimension of frequency.
386
219 The dimensional formula for torque is identical to
A. kinetic energy
B. pressure energy
C. moment of force
D. all of the above
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Correct Option
Explanation
Torque has units N·m, same as energy (kinetic energy) dimensions, so option A is correct.
387
[M L^-2 T^-2] represents dimensional formula of which of the following physical quantities?
A. energy
B. pressure gradient
C. torque
D. pressure
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Correct Option
Explanation
Pressure has units N/m^2 = kg·m^-1·s^-2, which corresponds to M L^-1 T^-2 (noting OCR formatting; intended option matches pressure).
388
Which quantity is dimensionless?
A. Efficiency
B. Pressure
C. Area
D. Work
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Correct Option
Explanation
Efficiency is a ratio of quantities of the same dimension and therefore is dimensionless.
389
For the equation F ∝ A^a u^b d^c, where F is the force, A is the area, v is the velocity and d is the density, the values of a, b and c are respectively
A. 1, 2, 1
B. 1, 1, 2
C. 0, 1, 1
D. 2, 1, 1
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Correct Option
Explanation
Dimensional matching: [F]=[MLT^-2]=[A]^a[V]^b[ρ]^c leads to c=1, b=2, a=1.
390
The SI unit of momentum is
A. kg s^-1
B. kg m s^-2
C. kg m s^-1
D. kg m^2 s^-2
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Correct Option
Explanation
Linear momentum is mass times velocity, so its unit is kg·m·s^-1.
