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Units and Dimensions

135 Questions Start Allen Test
All Exams Allen Objective Errorless
Q26 Allen 2. DIMENSIONS MCQ
Which of the following physical quantities has neither dimensions nor unit?
A.
angle
B.
Luminous intensity
C.
coefficient of friction
D.
Electric current
Q27 Allen 2. DIMENSIONS MCQ
Dimensions of relative density is
A.
kg m $^{-3}$
B.
[ML $^{-3}$ ]
C.
dimensionless
D.
[M $^{2}$ L $^{-6}$ ]
Q28 Allen 2. DIMENSIONS MCQ
Which of the following does not have dimensions of length?
A.
fermi
B.
micron
C.
angstrom
D.
radian
Q29 Allen 2. DIMENSIONS MCQ
The quantity having dimension -2 in the time is :-
A.
force
B.
pressure
C.
gravitational constant
D.
all of these
Q30 Allen 2. DIMENSIONS MCQ
The dimensional formula $[ML^{2}T^{-2}]$ represents :
A.
pressure
B.
linear momentum
C.
power
D.
energy
Q31 Allen 2. DIMENSIONS MCQ
Which pair has the same dimensions?
A.
Work and power
B.
Density and relative density
C.
Momentum and impulse
D.
Latent heat and specific heat
Q32 Allen 2. DIMENSIONS MCQ
Dimensions of one pair is same. Identify the pair:-
A.
Torque and energy
B.
Angular momentum and work
C.
Energy and pressure
D.
Light year and solar day
Q33 Allen 2. DIMENSIONS MCQ
The method of dimensional analysis can be used to derive which of the following relations?
A.
$N_{0}e^{-\lambda t}$
B.
A $\sin(\omega t + kx)$
C.
$\frac{1}{2}mv^{2} + \frac{1}{2}I\omega^{2}$
D.
None of the above
Q34 Allen 2. DIMENSIONS MCQ
If dimensions of A and B are different, then which of the following operation is valid?
A.
$\frac{A}{B}$
B.
$e^{-A/B}$
C.
A - B
D.
A + B
Q35 Allen 2. DIMENSIONS MCQ
Which of the following is incorrect statement
A.
A dimensionally correct equation may be correct
B.
A dimensionally correct equation may be incorrect
C.
A dimensionally incorrect equation may be correct
D.
A dimensionally incorrect equation is incorrect
Q36 Allen 2. DIMENSIONS MCQ
Which of the following is incorrect?
A.
All derived quantities may be represented dimensionally in terms of the base quantities
B.
A base quantity cannot be represented dimensionally in terms of other base quantities
C.
The dimension of a derived quantity is never zero in any base quantity
D.
The dimension of a base quantity in other base quantities is always zero.
Q37 Allen 2. DIMENSIONS MCQ
If $x = at + bt^{2}$ , where x is in metre and t is in hour(hr), then unit of b will be :-
A.
$m^{2}/hr$
B.
m
C.
m/hr
D.
$m/hr^{2}$
Q38 Allen 2. DIMENSIONS MCQ
A force is given by $\mathrm{F} = \mathrm{at} + \mathrm{bt}^2$ , where $t$ is time. The dimensions of $a$ and $b$ are
A.
[M L T-3] and [M L T-4]
B.
[M L T-4] and [M L T-3]
C.
[M L T-1] and [M L T-2]
D.
[M L T-2] and [M L T0]
Q39 Allen 2. DIMENSIONS MCQ
If $S = \frac{1}{3} ft^3$ , 'f' has the dimensions of - (S = distance, t = time)
A.
$[M^0 L^{-1} T^3]$
B.
$[M^1 L^1 T^{-3}]$
C.
$[M^0 L^1 T^{-3}]$
D.
$[M^0 L^{-1} T^{-3}]$
Q40 Allen 2. DIMENSIONS MCQ
The time dependence of a physical quantity P is given by $P = P_{0} \exp(-\alpha t^{2})$ , where $\alpha$ is a constant and t is time. The constant $\alpha$
A.
is dimensionless
B.
has dimensions $[T^{-2}]$
C.
has dimensions of P
D.
has dimensions $[T^{2}]$
Q41 Allen 2. DIMENSIONS MCQ
Given the force $F = Pt^{-1} + Qt$ . Here t is time. The unit of P is same as that of :-
A.
displacement
B.
velocity
C.
acceleration
D.
momentum
Q42 Allen 2. DIMENSIONS MCQ
The force F, on a sphere of radius 'a' moving in a medium with velocity v is given by $F = 6\pi\eta av$ . The dimensions of $\eta$ are:
A.
$[ML^{-1}T^{-1}]$
B.
$[MT^{-1}]$
C.
$[MLT^{-2}]$
D.
$[ML^{-3}]$
Q43 Allen 2. DIMENSIONS MCQ
The force is given in terms of time (t) and displacement (x) by the equation: $F = A \cos Bx + C \sin Dt$ Then, the dimensions of $\frac{D}{B}$ are :-
A.
$M^{o}L^{o}T^{o}$
B.
$M^{o}L^{o}T^{-1}$
C.
$M^{o}L^{-1}T^{o}$
D.
$M^{o}LT^{-1}$
Q44 Allen 2. DIMENSIONS MCQ
For a body moving along x-axis, the distance travelled by body from a reference point is given as function of time t as $x = at^{2} + b$ , where a and b are constants, then the dimension of $\sqrt{ab}$ is same as :-
A.
speed
B.
distance travelled
C.
acceleration
D.
none of these
Q45 Allen 2. DIMENSIONS MCQ
In the relation $y = r \sin (\omega t - kx)$ the dimensions of $\frac{\omega}{k}$ are:-
A.
$[M^0 L^1 T^0]$
B.
$[M^0 L^1 T^{-1}]$
C.
$[M^0 L^0 T^3]$
D.
$[M^0 L^1 T^0]$
Q46 Allen 2. DIMENSIONS MCQ
A wave is represented by $y = a \sin (At - Bx + C)$ where A, B, C are constants. The dimensions of A, B, C are
A.
$T^{-1}$ , L, $M^{0}L^{0}T^{0}$
B.
$T^{-1}$ , $L^{-1}$ , $M^{0}L^{0}T^{0}$
C.
T, L, M
D.
$T^{-1}$ , $L^{-1}$ , $M^{-1}$
Q47 Allen 2. DIMENSIONS MCQ
For $10^{(at+3)}$ , the dimensions of a is :-
A.
$M^{0}L^{0}T^{0}$
B.
$M^{0}L^{0}T^{1}$
C.
$M^{0}L^{0}T^{-1}$
D.
None of these
Q48 Allen 2. DIMENSIONS MCQ
The equation $\frac{\mathrm{d}v}{\mathrm{d}t} = AT - Bv$ is describing the rate of change of velocity of a body falling from rest in a resisting medium. The dimensions of A and B are :-
A.
$\mathrm{LT^{-3}}$ , T
B.
$\mathrm{LT^{-3}}$ , $\mathrm{T^{-1}}$
C.
LT, T
D.
LT, $\mathrm{T^{-1}}$
Q49 Allen 2. DIMENSIONS MCQ
If y represents distance and x-represents time, dimensions of $\frac{d^{2}y}{dx^{2}}$ are :-
A.
LT $^{-1}$
B.
L $^{2}$ T $^{2}$
C.
L $^{2}$ T $^{-1}$
D.
LT $^{-2}$
Q50 Allen 2. DIMENSIONS MCQ
If energy (E), velocity (v) and force (F), be taken as fundamental quantities, then what are the dimensions of mass :-
A.
EV $^{2}$
B.
EV $^{-2}$
C.
FV $^{-1}$
D.
FV $^{-2}$