Physics - Units Measurement - Quiz-11

If the dimension of a physical quantity are given by $M^{a} L^{b} T^{c},$ then the physical quantity will be

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pressure if a=1, b=-1, c=-2
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velocity if a=1, b=0, c=-1
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acceleration if a=1, b=1,c=-2
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force if a=0, b=-1, c=-2

If the error in the measurement of the radius of a sphere is 2%, then the error in the determination of the volume of the sphere will be:

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4%
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6%
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8%
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2%

Which two of the following five physical parameters have the same dimensions ?

(1) energy density

(2) refractive index

(3) dielectric constant

(4) Young's modulus

(5) magnetic field

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2 and 4
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3 and 5
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1 and 4
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1 and 5

Consider the following equation of Bernoulli’s theorem-

$P + \frac{1}{2} {ρV}^{2} + ρgh = K (constant)$

The dimensions of K/P are the same as that of which of the following?

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Angle
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Viscosity
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Thrust
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Pressure

In a vernier calliper, N divisions of vernier scale coincides with (N-1) divisions of the main scale (in which length of one division is 1 mm). The least count of the instrument should be:

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$N mm$
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$(N - 1) mm$
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$\frac{1}{10 N} cm$
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$\frac{1}{(N - 1)} mm$

In certain vernier callipers, 25 divisions on vernier scale have same length as 24 divisions on main scale. One division on main scale is 1 mm long. The least count of the instrument is

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0.04 mm
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0.01 mm
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0.02 mm
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0.08 mm

One centimeter on the main scale of Vernier calliper is divided into ten equal parts. If 10 divisions of Vernier scale coincide with 8 small divisions of the main scale, the least count of the callipers is:

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0.01 cm
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0.02 cm
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0.05 cm
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0.07 cm

A Screw Guage gives the following readings when used to measure the diameter of a wire.
Main scale reading = 0.0 mm
Circular scale reading = 52 divisions
Given that: 1 mm on the main scale corresponds to 100 divisions of the circular scale.
The diameter of the wire from the above data is:

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0.026 cm
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0.005 cm
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0.52 cm
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0.052 cm

Two full turns of the circular scale of gauge cover a distance of 1 mm on scale. The total number of divisions on circular scale is 50. Further, it is found that screw gauge has a zero error of -0.03 mm. While measuring the diameter of a thin wire a student notes the main scale reading of 3 mm and the number of circular scale division in line, with the main scale as 35. The diameter of the wire is

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3.32 mm
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3.73 mm
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3.67 mm
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3.38 mm

The circular division of shown screw gauge are 50. It moves 0.5 mm on main scale in one rotation. The diameter of the ball is

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2.25 mm
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2.20 mm
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1.20 mm
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1.25 mm

The pitch of a screw gauge is 1.0 mm and there are 100 divisions on the circular scale. While measuring the diameter of a wire, the linear scale reads 1 mm and the 47^th division on the circular scale coincides with the reference line. The length of the wire is 5.6 cm. Find the wire's curved surface area (in cm²) in an appropriate number of significant figures.

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2.4 cm²
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2.56 cm²
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2.6 cm²
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2.8 cm²

Consider a screw gauge without any zero error. What will be the final reading corresponding to the final state as shown? It is given that the circular head translates P MSD in N rotations. One MSD is equal to 1 mm.

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$(\frac{P}{N}) (2 + \frac{45}{100}) mm$
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$(\frac{N}{P}) (2 + \frac{45}{N}) mm$
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$P (\frac{2}{N} + \frac{45}{100}) mm$
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$(2 + \frac{45}{100} \times \frac{P}{N}) mm$

A screw gauge has some zero error but its value is unknown. We have two identical rods. When the first rod is inserted in the screw, the state of the instrument is shown by diagram (I). When both the rods are inserted together in series then the state is shown by the diagram (II). What is the zero error of the instrument? 1 msd = 100 csd = 1 mm

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-0.16 mm
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+0.16 mm
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+0.14 mm
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-0.14 mm

Find the zero correction in the given figure.

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0.4 mm
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0.5 mm
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-0.5 mm
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-0.4 mm

Find the thickness of the wire. The least count is 0.01 mm. The main scale reads in mm.

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7.62 mm
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7.63 mm
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7.64 mm
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7.65 mm

The value of 60 $°$ in radian is

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$\frac{π}{2}$
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$\frac{π}{3}$
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$\frac{π}{4}$
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$\frac{π}{5}$

The total plane angle subtended by a circle at its centre is

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$π r a d$
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$2 π r a d$
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$\frac{2 π}{3} r a d$
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$\frac{π}{2} r a d$

In the given Vernier scale, 10 divisions of the vernier scale is matching with 9 divisions of the main scale as shown in the first figure. Find the diameter of the object in the second figure. Assume the edge of the vernier as '0' of the vernier.

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15.6 mm
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156 mm
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1.56 mm
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0.156 mm

The main scale of a vernier callipers reads 10 mm in 10 divisions. 10 divisions of Vernier scale coincide with 9 divisions of the main scale. When the two jaws of the callipers touch each other, the fifth division of the vernier coincides with 9 main scale divisions and the zero of the vernier is to the right of zero of main scale. When a cylinder is tightly placed between the two jaws, the zero of vernier scale lies slightly behind 3.2 cm and the fourth vernier division coincides with a main scale division. The diameter of the cylinder is.

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3.10 cm
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3.8 cm
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3.09 cm
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-3.09 cm

A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm. The main scale reading is 5 mm and zero of circular scale division coincides with 25 divisions above the reference level. If screw gauge has a zero error of –0.004 cm, the correct diameter of the ball is:

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0.521 cm
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0.525 cm
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0.053 cm
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0.529 cm

If energy (E), velocity (v) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be:

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[Ev^-2T^-1]
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[Ev^-1T^-2]
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[Ev^-2T^-2]
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[E^-2v^-1T^-3]

In an experiment, four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows :
P =

\frac{a^{3} b^{2}}{c d}

Percentage error in P is :

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10%
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7%
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4%
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14%

The dimensions of ${(μ_{0} ε_{0})}^{- 1 / 2}$ are

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$[L^{- 1} T]$
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$[{LT}^{- 1}]$
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$[L^{- 1 / 2} T^{1 / 2}]$
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$[L^{- 1 / 2} T^{- 1 / 2}]$

If the dimensions of a physical quantity are given by M^aL^bT^c, then the physical quantity will be:

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Pressure if a = 1, b = -1, c = - 2
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Velocity if a = 1, b = 0, c = - 1
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Acceleration if a = 1, b = 1, c = - 2
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Force if a = 0, b =-1, c = - 2

Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, length L, time T and current I, would be:

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$[{ML}^{2} T^{- 3} I^{- 1}]$
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$[{ML}^{2} T^{- 2}]$
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$[{ML}^{2} T^{- 1} I^{- 1}]$
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$[{ML}^{2} T^{- 3} I^{- 2}]$

The velocity v of a particle at time t is given by $v = a t + \frac{b}{t + c}$ , where a, b and c are constants. The dimensions of a, b, and c are respectively:

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$[{LT}^{- 2}], [L] and [T]$
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$[L^{2}], [T] and [{LT}^{2}]$
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$[{LT}^{2}], [LT] and [L]$
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$[L], [LT] and [T^{2}]$

The unit of thermal conductivity is:

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$W m^{- 1} K^{- 1}$
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$J m K^{- 1}$
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$J m^{- 1} K^{- 1}$
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$W m K^{- 1}$

In an experiment, the percentage errors that occured in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then, the maximum percentage of error in the measurement of X, where $X = \frac{A^{2} B^{\frac{1}{2}}}{C^{\frac{1}{3}} D^{3}}$ , will be:

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10%
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$(\frac{3}{13}) %$
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16%
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-10%

A physical quantity X depends on four measurables a, b, c, and d as X =

\frac{a^{2} b^{3}}{c^{5} d}

. To ensure maximum accuracy in the determination of X, the quantity that should be measured with maximum accuracy is :

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a
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b
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c
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d

If z= $\frac{A \times B}{A + B}$ , and errors in the determination of A and B are respectively $△ A and △ B$ , then the fractional error in the calculation of z is :

$1 . \frac{Δ A}{A} + \frac{Δ B}{B} + \frac{Δ A + Δ B}{A + B} 2 . \frac{Δ A}{A} + \frac{Δ B}{B} - \frac{(Δ A + Δ B)}{A + B} 3 . \frac{Δ A}{A} + \frac{Δ B}{B} 4 . Z e r o$

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1
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2
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3
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4

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Practice Physics Quiz Questions and Answers

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Practice Physics Quiz Questions and Answers

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