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Units and Dimensions

135 Questions Start Allen Test
All Exams Allen Objective Errorless
Q101 Allen 5. PYQ MCQ
Taking into account of the significant figures, what is the value of 9.99 m - 0.0099 m?
A.
9.9 m
B.
9.9801 m
C.
9.98 m
D.
9.980 m
Q102 Allen 5. PYQ MCQ
Dimensions of stress are:
A.
$[M\ L^{-1}\ T^{-2}]$
B.
$[M\ L\ T^{-2}]$
C.
$[M\ L^{2}\ T^{-2}]$
D.
$[M\ L^{0}\ T^{-2}]$ PP
Q103 Allen 5. PYQ MCQ
A screw gauge has least count of 0.01 mm and there are 50 divisions in its circular scale. The pitch of the screw gauge is :
A.
1.0 mm
B.
0.01 mm
C.
0.25 mm
D.
0.5 mm
Q104 Allen 5. PYQ MCQ
The angle of $1'$ (minute of arc) in radian is nearly equal to
A.
$2.91 \times 10^{-4}$ rad
B.
$4.85 \times 10^{-4}$ rad
C.
$4.80 \times 10^{-6}$ rad
D.
$1.75 \times 10^{-2}$ rad
Q105 Allen 5. PYQ MCQ
Time intervals measured by a clock give the following readings: 1.25 s, 1.24 s, 1.27 s, 1.21 s and 1.28 s. What is the percentage relative error of the observations?
A.
2 %
B.
4 %
C.
16 %
D.
1.6 %
Q106 Allen 5. PYQ MCQ
If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy.
A.
[F] [A] [T]
B.
[F] [A] [T $^{2}$ ]
C.
[F] [A] [T $^{-1}$ ]
D.
[F] [A $^{-1}$ ] [T]
Q107 Allen 5. PYQ MCQ
A screw gauge gives the following readings when used to measure the diameter of a wire Main scale reading : 0 mm Circular scale reading : 52 divisions Given that 1 mm on main scale corresponds to 100 divisions on the circular scale. The diameter of the wire from the above data is :
A.
0.52 cm
B.
0.026 cm
C.
0.26 cm
D.
0.052 cm
Q108 Allen 5. PYQ MCQ
If E and G respectively denote energy and gravitational constant, then $\frac{E}{G}$ has the dimensions of:
A.
$[M^{2}]$ $[L^{-1}]$ $[T^{0}]$
B.
$[M]$ $[L^{-1}]$ $[T^{-1}]$
C.
$[M]$ $[L^{0}]$ $[T^{0}]$
D.
$[M^{2}]$ $[L^{-2}]$ $[T^{-1}]$
Q109 Allen 5. PYQ MCQ
Plane angle and solid angle have :
A.
Dimensions but no units
B.
No units and no dimensions
C.
Both units and dimensions
D.
Units but no dimensions
Q110 Allen 5. PYQ MCQ
The dimensions $\left[\mathrm{MLT}^{-2}\mathrm{A}^{-2}\right]$ belong to the :
A.
self inductance
B.
magnetic permeability
C.
electric permittivity
D.
magnetic flux
Q111 Allen 5. PYQ MCQ
The physical quantity that has the same dimensional formula as pressure is :
A.
Force
B.
Momentum
C.
Young's modulus of elasticity
D.
Coefficient of viscosity
Q112 Allen 5. PYQ MCQ
The ratio of coulomb's electrostatic force to the gravitational force between an electron and a proton separated by some distance is $2.4 \times 10^{39}$ . The ratio of the proportionality constant, $K = \frac{1}{4\pi\varepsilon_{0}}$ to the Gravitational constant G is nearly (Given that the charge of the proton and electron each $= 1.6 \times 10^{-19}$ C, the mass of the electron $= 9.11 \times 10^{-31}$ kg, the mass of the proton $= 1.67 \times 10^{-27}$ kg):
A.
$10^{20}$
B.
$10^{30}$
C.
$10^{40}$
D.
10
Q113 Allen 5. PYQ MCQ
The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are :
A.
Personal errors
B.
Least count errors
C.
Random errors
D.
Instrumental errors
Q114 Allen 5. PYQ MCQ
A metal wire has mass $(0.4 \pm 0.002)$ g, radius $(0.3 \pm 0.001)$ mm and length $(5 \pm 0.02)$ cm. The maximum possible percentage error in the measurement of density will nearly be:
A.
1.3%
B.
1.6%
C.
1.4%
D.
1.2%
Q115 Allen 5. PYQ MCQ
The diameter of a spherical bob, when measured with vernier callipers yielded the following values: 3.33 cm, 3.32 cm, 3.34 cm, 3.33 cm and 3.32 cm. The mean diameter to appropriate significant figures is:
A.
3.328 cm
B.
3.3 cm
C.
3.33 cm
D.
3.32 cm
Q116 Allen 5. PYQ MCQ
The mechanical quantity, which has dimensions of reciprocal of mass (M $^{-1}$ ) is :
A.
angular momentum
B.
coefficient of thermal conductivity
C.
torque
D.
gravitational constant
Q117 Allen 5. PYQ MCQ
In a vernier calipers, $(N+1)$ divisions of vernier scale coincide with N divisions of main scale. If 1 MSD represents 0.1 mm, the vernier constant (in cm) is:
A.
$\frac{1}{10N}$
B.
$\frac{1}{100(N+1)}$
C.
100N
D.
10(N+1)
Q118 Allen 5. PYQ MCQ
The quantities which have the same dimensions as those of solid angle are:
A.
strain and angle
B.
stress and angle
C.
strain and arc
D.
angular speed and stress
Q119 Allen 5. PYQ MCQ
A force defined by $\mathrm{F} = \alpha t^2 + \beta t$ acts on a particle at a given time $t$ . The factor which is dimensionless, if $\alpha$ and $\beta$ are constants, is:
A.
$\frac{\beta t}{\alpha}$
B.
$\frac{\alpha t}{\beta}$
C.
$\alpha \beta t$
D.
$\frac{\alpha \beta}{t}$
Q120 Allen 5. PYQ MCQ
In an electrical circuit, the voltage is measured as $V = (200 \pm 4)$ volt and the current is measured as $I = (20 \pm 0.2)$ A. The value of the resistance is:
A.
$(10 \pm 4.2)\Omega$
B.
$(10 \pm 0.3)\Omega$
C.
$(10 \pm 0.1)\Omega$
D.
$(10 \pm 0.8)\Omega$
Q121 Allen 5. PYQ MCQ
The pitch of an error free screw gauge is 1 mm and there are 100 divisions on the circular scale. While measuring the diameter of a thick wire, the pitch scale reads 1 mm and 63 $^{rd}$ division on the circular scale coincides with the reference line. The diameter of the wire is:
A.
1.63 cm
B.
0.163 cm
C.
0.163 m
D.
1.63 m
Q122 Allen 5. PYQ MCQ
The potential energy of a particle moving along x-direction varies as $V = \frac{Ax^{2}}{\sqrt{x} + B}$ . The dimensions of $\frac{A^{2}}{B}$ are :
A.
$[M^{3/2} L^{1/2} T^{-3}]$
B.
$[M^{1/2} L T^{-3}]$
C.
$[M^{2} L^{1/2} T^{-4}]$
D.
$[M L^{2} T^{-4}]$
Q123 Allen 6. ANALYTICAL QUESTIONS MCQ
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Absolute error in a physical quantity may be +ve, -ve or zero.
Reason (R) : Absolute error is the difference of measured value and true value of a physical quantity.
In the light of the above statements,
choose the most appropriate answer from the options given below:
A.
Both (A) and (R) are true and (R) is the correct explanation of (A).
B.
Both (A) and (R) are true and (R) is NOT the correct explanation of (A).
C.
(A) is true but (R) is false.
D.
(A) is false but (R) is true.
Q124 Allen 6. ANALYTICAL QUESTIONS MCQ
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Maximum possible error in a reading is taken as least count of the measuring instrument.
Reason (R) : Error in a measurement can not be greater than least count of the measuring instrument.
In the light of the above statements,
choose the most appropriate answer from the options given below:
A.
Both (A) and (R) are true and (R) is the correct explanation of (A).
B.
Both (A) and (R) are true and (R) is NOT the correct explanation of (A).
C.
(A) is true but (R) is false.
D.
(A) is false but (R) is true.
Q125 Allen 6. ANALYTICAL QUESTIONS MCQ
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Higher is the accuracy of measurement, if instrument has smaller least count.
Reason (R) : Smaller the percentage error, higher is the accuracy of measurement.
In the light of the above statements,
choose the most appropriate answer from the options given below:
A.
Both (A) and (R) are true and (R) is the correct explanation of (A).
B.
Both (A) and (R) are true and (R) is NOT the correct explanation of (A).
C.
(A) is true but (R) is false.
D.
(A) is false but (R) is true.