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Practice Exercise¶

A nanosecond is:
$10^9 s$
$10^{-10} s$
$10^{-1}s$
$10^{-9}s$
Ans: $10^{-9}s$
The dimension of energy density is same as that of
Pressure
Force
(velocity)$^2$
Acceleration
Ans: Pressure
The quantities $L/R$ and $RC$ (where $L$, $C$ and $R$ stand for inductance, capacitance and resistance respectively) have the same dimensions as those of
Velocity
Acceleration
Time
Force
Ans: Time
Which pair of quantities has dimensions different from the other three pairs?
Impulse and linear momentum
Plank's constant and angular momentum
Moment of inertia and moment of force
Young's modulus and pressure
Ans: Moment of inertia and moment of force
In scientific notation numbers are expressed in
Power of ten
Powers of two
Reciprocal
Decimal
Ans: Power of ten
1024 can be written in scientific notation as
$1.024\times 10^3$
$21^3$
$0.000976$
$1/0.00097$
Ans: $1.024\times 10^3$
The dimensions of plank's constant are the same as those of
Energy
Power
Angular frequency
Angular momentum
Ans: Angular momentum
The density of a cube is measured by measuring its mass and the length of its side. If the maximum errors in the measurement of mass and length are 3% and 2%, respectively the maximum error in the measurement of density is
$1$%
$5$%
$7$%
$9$%
Ans: $9$%
The uncertainty in a measurement may occur due to
Limitation of an instrument
Natural variation of the object to be measured
Inadequate technique
All given in a, b and c
Ans: All given in a, b and c
Which of the following quantities has not been expressed in the proper per units?
Young's modulus $=Nm^{-2}$
Surface Tension $=Nm^{-1}$
Pressure $=Nm^{-2}$
Energy $=Kgms^{-1}$
Ans: Energy $=Kgms^{-1}$
One nanometer is equal to
$10^9 mm$
$10^{-6} cm$
$10^{-7} cm$
$10^{-9} cm$
Ans: $10^{-7} cm$
A digit zero in a measurement
May be significant or may not be significant
Always significant
Always insignificant
Significant only if left to a significant figure
Ans: May be significant or may not be significant
Number of significant figures in $0.0173$ are
Three
Four
Five
Two
Ans: Three
Smaller the least count of the instrument more is the measurement
Accurate
Precise
Accurate and precise
None of these
Ans: Precise
The number of significant figures in $15.0$ is/are
$2$
$6$
$1$
$3$
Ans: $3$
When comparing systematic and random errors, the following pairs errors in an experimental measurement may be contrasted:
- $P_1$: error can possibly be eliminated
- $P_2$: error cannot possibly be eliminated
- $Q_1$: error is of constant sign and magnitude
- $Q_2$: error is of varying sign and magnitude
- $R_1$: error will be reduced by averaging repeated measurement
- $R_2$: error will not be reduced by averaging repeated measurements
Which properties apply to random error?
$P_1$, $Q_1$, $R_2$
$P_2$. $Q_2$, $R_1$
$P_1$. $Q_2$, $R_2$
$P_2$. $Q_1$, $R_1$
Ans: $P_2$. $Q_1$, $R_1$
Dimensional analysis is helpful for
Deriving a possible formula
Checking the homogeneity of a physical equation
Verification of laws
Only a and b are correct
Ans: Only a and b are correct
Which equation is not dimensionally correct?
$E=mc^2$
$v_t=v_i+at$
$S=vt^2$
$S=\frac{1}{2}at^2$
Ans: $S=vt^2$
SI unit of coefficient of viscosity is
$kgms^{-1}$
$kg m^{-1} s^{-1}$
$kg m s$
$kg^{-1} m^{-1} s^{-1}$
Ans: $kg m^{-1} s^{-1}$
Three students measured length of a needle with meter rod and recorded as:
- $0.2145m$
- $0.21m$
- $0.214m$
Which one is correct record?
Only (i)
Only (ii)
Only (iii)
Both (i) and (ii)
Ans: Only (iii)
A force $F$ is applied on a square plate of side $L$. If the percentage error in the determination of $L$ is $2$% and that in $F$ is $4$%, maximum error in pressure is
$2$%
$4$%
$6$%
$8$%
Ans: $8$%
The energy of a photon of light of frequency $f$ is given by $hf$, where here h is the Planck constant. What are the base units of $h$?
$kg m s^{-1}$
$kg m^2 s^{-1}$
$kg m^2 S^{-2}$
$kg m^2 s^{-3}$
Ans: $kg m^2 s^{-1}$
Steradian is the SI unit of
Plane angle
Solid angle
Both plane angle and solid angle
Neither plane angle nor solid angle
Ans: Solid angle
Which pair has same dimension
Work, torque
Work, energy
Energy, torque
All are correct
Ans: All are correct
Which experimental technique reduces the systematic error of the quantity being investigated?
Adjusting an ammeter to remove its zero error below measuring a current
Measuring several inter-nodal distance on a standing wave to find the mean inter-nodal distance
Measuring the diameter of a wire repeatedly and calculating the average
Timing a large number of oscillations to find a period
Ans: Adjusting an ammeter to remove its zero error below measuring a current
In multiplication and division of measurement
Percentage uncertainties arc added
Absolute uncertainties are added
Percentage uncertainties are divided
Absolute uncertainties are divided
Ans: Percentage uncertainties arc added
The number of significant figures in $5,400$ are
Three
Five
Two
Four
Ans: Four
Which of the following could be measured in the same units as force?
Momentum $\times$ distance
Energy $\times$ distance
Energy $/$ time
Energy $/$ distance
Ans: Energy $/$ distance
The number of significant figures in the length of a bar $9800mm$ measured by meter rod are
Four
Three
Two
None of these
Ans: Four
A radio aerial of length $L$, when the current is $I$, emits a signal of wavelength $\lambda$ and power $P$. These quantities are related by $$ P=kl\left(\frac{L}{\lambda}\right)^2 $$ Where $k$ is a constant. What unit, if any, should be used for the constant $k$?
Volt
Watt
Ohm
No unit
Ans: Ohm
Dimension of resistance

$[M^1L^2T^{-2}A^{-2}]$
$[M^1L^{-2}T^{-3}A^{-2}]$
$[M^1L^2T^{-2}A^{-2}]$
$[MT^{-2}]$
Ans: $[M^1L^2T^{-2}A^{-2}]$

Practice Exercise¶

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