Chapter 1

The SI unit of electrochemical equivalent is (a) \(\mathrm{kg} \mathrm{C}\) (b) \(\mathrm{C} \mathrm{kg}^{-1}\) (c) \(\mathrm{kg} \mathrm{C}^{-1}\) (d) \(\mathrm{kg}^{2} \mathrm{C}^{-1}\)

The sum of numbers 436.32, \(227.2\) and \(0.301\) in appropriate significant figures in (a) \(663.821\) (b) 664 (c) \(663.8\) (d) \(663.82\)

In the equation \(X=3 Y Z^{2}, X\) and \(Z\) have dimensions of capacitance and magnetic induction respectively. In MKSQ system, the dimensional formula of \(Y\) is (a) \(\left[\mathrm{M}^{-3} \mathrm{~L}^{-2} \mathrm{~T}^{-2} \mathrm{Q}^{-4}\right]\) (b) \(\left[\mathrm{ML}^{-2}\right]\) (c) \(\left[\mathrm{M}^{-3} \mathrm{~L}^{-2} \mathrm{Q}^{4} \mathrm{~T}^{8}\right]\) (d) \(\left[\mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{Q}^{4} \mathrm{~T}^{4}\right]\)

Given that \(r=m^{2} \sin p t\), where \(t\) represents time. If the unit of \(m\) is \(\mathrm{N}\), then the unit of \(r\) is (a) \(N\) (b) \(\mathrm{N}^{2}\) (c) \(\mathrm{N}\)-s (d) \(\mathrm{N}^{2} \mathrm{~s}\)

When a wave transverses a medium the displacement of a particle located at \(x\) at a time \(t\) is given by \(y=a \sin (b t-c x)\), where \(a, b\) and \(c\) are constants of the wave. Which of the following is dimensionless? \(\begin{array}{llll}\text { (a) } \frac{y}{a} & \text { (b) } b t & \text { (c) } c x & \text { (d) } \frac{b}{c}\end{array}\)

A pressure of \(10^{6}\) dyne \(\mathrm{cm}^{-2}\) is equivalent to (a) \(10^{5} \mathrm{Nm}^{-2}\) (b) \(10^{4} \mathrm{Nm}^{-2}\) (c) \(10^{6} \mathrm{Nm}^{-2}\) (d) \(10^{7} \mathrm{Nm}^{-2}\)

In a new system of units, unit of mass is \(10 \mathrm{~kg}\), unit of length is \(1 \mathrm{~km}\) and unit of time is \(1 \mathrm{~min}\). The value of \(1 \mathrm{~J}\) in this new hypothartical system is (a) \(3.6 \times 10^{-4}\) new units (b) \(6 \times 10^{7}\) new units (c) \(10^{11}\) new units (d) \(1.67 \times 10^{4}\) new units

Universal time is based on (a) rotation of earth on its axis (b) oscillations of quartz crystal (c) vibrations of cesium atom (d) earth's orbital motion around the sun

\(\left[\mathrm{ML}^{3} \mathrm{~T}^{-1} \mathbf{Q}^{-1}\right]\) is the dimensional formula of (a) resistance (b) resistivity (c) capacitance (d) conductivity

Which of the following cannot be regarded as an essential characteristic of a unit of measurement? (a) Inaccessibility (b) Indenstructibility (c) Invariability (d) Reproductibility

The number of particles given by \(n=D \frac{n_{2}-n_{1}}{x_{2}-x_{1}}\) are crossing a unit area perpendicular to \(x\)-axis in unit time, where \(n_{1}\) and \(n_{2}\) are the number of particles per unit volume for the values \(x_{1}\) and \(x_{2}\) of \(x\) respectively. Then the dimensional formula of diffusion constant \(D\) is (a) \(\left[\mathrm{M}^{0} \mathrm{LT}^{0}\right]\) (b) \(\left[\mathrm{M}^{0} \mathfrak{2}^{2} \mathrm{~T}^{-4}\right]\) (c) \(\left[\mathrm{M}^{0} \mathrm{LT}^{-3}\right]\) (d) \(\left[\mathrm{M}^{0}{\underline{\phantom{xx}}}^{2} \mathrm{~T}^{-1}\right]\)

Young modulus of steel is \(1.9 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}\). When expressed in CGS units of dyne \(/ \mathrm{cm}^{2}\), it will be equal to \(\left(1 \mathrm{~N}=10^{5}\right.\) dyne, \(1 \mathrm{~m}^{2}=10^{4} \mathrm{~cm}^{2}\) ) (a) \(1.9 \times 10^{10}\) (b) \(1.9 \times 10^{11}\) (c) \(1.9 \times 10^{12}\) (d) \(1.9 \times 10^{13}\)

The dimensional formula of \(\frac{1}{\varepsilon_{0}} \frac{e^{2}}{h c}\) is (a) \(\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0} \mathrm{~A}^{0}\right]\) (b) \(\left[\mathrm{M}^{-} \mathrm{L}^{3} \mathrm{~T}^{2} \mathrm{~A}\right]\) (c) \(\left[\mathrm{ML}^{3} \mathrm{~T}^{-4} \mathrm{~A}^{-2}\right]\) (d) \(\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^{4}\right]\)

Which one of the following pairs of quantities and their unit is properly matched? (a) Electric field-coulomb/m (b) Magnetic flux- Weber/m? (c) Power-Farad 1(d) Capacitance-Henry

The radius of the proton is about \(10^{-15} \mathrm{~m}\). The radius of the observable universe is \(10^{26} \mathrm{~m}\). Identify the distance which is half-way between, these two extremes on a logarithmic scale. (a) \(10^{21} \mathrm{~m}\) (b) \(10^{6} \mathrm{~m}\) (c) \(10^{-6} \mathrm{~m}\) (d) \(10^{0} \mathrm{~m}\)

The mean length of an object is \(5 \mathrm{~cm}\). Which is the following measurements is most accurate? [NCERT Exemplar] (a) \(4.9 \mathrm{~cm}\) (b) \(4.805 \mathrm{~cm} \quad\) (c) \(5.25 \mathrm{~cm}\) (d) \(5.4 \mathrm{~cm}\)

Given \(X=\left(G h / c^{3}\right)^{1 / 2}\), where \(G, h\) and \(c\) are gravitational constant, Planck's constant and the velocity of light respectively. Dimensions of \(X\) are the same as those of (a) mass (b) time (c) length (d) acceleration

The dimensional formula of coefficient of permittivity for free space \(\left(\varepsilon_{0}\right)\) is (a) \(\left[\mathrm{ML}^{3} \mathrm{~A}^{-2} \mathrm{~T}^{-4}\right]\) (b) \(\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^{4} \mathrm{~A}^{2}\right]\) (c) \(\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~A}^{-2} \mathrm{~T}^{-4}\right]\) (d) \(\left[M L^{3} A^{2} T^{-4}\right]\)

Which of the following pairs of physical quantities does not have same dimensional formula? [NCERT] (a) Work and torque (b) Angular momentum and Planck's constant (c) Tension and surface tension (d) Impulse and linear momentum

The surface tension of mercury is 32 dyne \(\mathrm{cm}^{-1}\). Its value in SI units is (a) \(0.032\) (b) \(0.32\) (c) 3200 (d) 32000

What is the unit of \(k\) in the relation where, \(U=\frac{k y}{y^{2}+a^{2}}\) where \(U\) represents the potential energy, \(y\) represents the displacement and \(a\) represents amplitude? (a) \(\mathrm{m} \mathrm{s}^{-1}\) (b) \(\overline{m s}\) (c) \(\mathrm{Jm}\) (d) \(\mathrm{J} \mathrm{s}^{-1}\)

In the relation \(y=r \sin (\omega t-k x)\), the dimensional formula of \(\omega / k\) are (a) \(\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}\right]\) (b) \(\left[\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{-1}\right]\) (c) \(\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{\mathrm{T}}\right]\) (d) \(\left[\mathrm{M}^{0} \mathrm{~L}^{\mathrm{l}} \mathrm{T}^{\mathrm{O}}\right]\)

One light year is defined as the distance travelled by light in one year. The speed of light \(3 \times 10^{8} \mathrm{~ms}^{-1}\). The same in metre is (a) \(3 \times 10^{12} \mathrm{~m}\) (b) \(9.461 \times 10^{15} \mathrm{~m}\) (c) \(3 \times 10^{15} \mathrm{~m}\) (d) None of these

Let us choose a new unit of length such that the velocity of light in vacuum is unity. If light takes 8 min and \(20 \mathrm{~s}\) to cover the distance between sun and earth, this distance in terms of the new unit is (a) 5 (b) 50 (c) 500 (d) \(3 \times 10^{8}\)

One slug is equivalent to \(14.6 \mathrm{~kg}\). A force of 10 pound is applied on a body of \(1 \mathrm{~kg}\). The acceleration of the body is (a) \(44.5 \mathrm{~ms}^{-2}\) (b) \(4.448 \mathrm{~ms}^{-2}\) (c) \(44.4 \mathrm{~ms}^{-2}\) (d) None of these

If the acceleration due to gravity is \(10 \mathrm{~ms}^{-2}\) and the units of length and time are changed in kilometre and hour respectively, the numerical value of acceleration is (a) 360000 (b) 72000 (c) 36000 (d) 129600

An important milestone in the evolution of the universe just after the Big Bang is the Planck time \(t_{p}\), the value of which depends on three fundamental constants speed \(c\) of light in vacuum, gravitational constant \(G\) and Planck's constant \(h\). Then, \(t_{p} \propto\) (a) \(\mathrm{Ghc}^{5}\) (b) \(\frac{c^{5}}{G h}\) (c) \(\frac{G h}{c^{5}}\) (d) \(\left(\frac{G h}{c^{5}}\right)^{1 / 2}\)

One amu is equivalent to \(931 \mathrm{MeV}\) energy. The rest mass of electron is \(9.1 \times 10^{-31} \mathrm{~kg}\). The mass energy is (1 amu \(=1.67 \times 10^{-17} \mathrm{~kg}\) ) (a) \(0.5073 \mathrm{MeV}\) (b) \(0.693 \mathrm{MeV}\) (c) \(4.0093 \mathrm{MeV}\) (d) None of these

If \(1 \mathrm{~g} \mathrm{~cm} \mathrm{~s}^{-1}=x\) newton-sec, then the number \(x\) is equal to (a) \(1 \times 10^{-3}\) (b) \(3.6 \times 10^{-3}\) (c) \(1 \times \underline{10^{-5}}\) (d) \(6 \times \underline{10^{-4}}\)

The value of universal gas constant is \(R=8.3 \mathrm{~J} / \mathrm{k}-\mathrm{mol}\). The value of \(R\) in atmosphere litre per kelvin per mol (a) \(8.12\) (b) \(0.00812\) (c) \(81.2\) (d) \(0.0812\)

The frequency of vibration \(f\) of a mass \(m\) suspended from a spring of spring constant \(k\) is given by relation of the type \(f=c m^{x} k^{y}\), where \(c\) is a dimensionless constant. The values of \(x\) and \(y\) are (a) \(1 / 2,1 / 2\) (b) \(-1 / 2,-1 / 2\) (c) \(1 / 2,-1 / 2\) (d) \(-1 / 2,1 / 2\)

Electron-volt is the unit of energy \(\left(1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J}\right) .\) In \(\mathrm{H}\)-atom, the binding energy of electron in first orbit is \(13.6 \mathrm{eV}\). The same in joule (J) is (a) \(10 \times 10^{-19} \mathrm{~J}\) (b) \(21.76 \times 10^{-19} \mathrm{~J}\) (c) \(13.6 \times 10^{-19} \mathrm{~J}\) (d) None of these

What will be the unit of time in that system in which the unit of length is metre, unit of mass is \(\mathrm{kg}\) and unit of force is kg-wt? (a) \((9.8)^{2} \mathrm{~s}\) (b) \(9.8 \mathrm{~s}\) (c) \(\sqrt{9.8} \mathrm{~s}\) (d) \(\frac{1}{\sqrt{9.8}} 5\)

The expression for centripetal force \((F)\) depends upon mass of body \((m)\), speed \((v)\) of the body and the radius ( \(r\) ) of circular path will be expression for centripetal force (a) \(F=\frac{m v^{2}}{2 r^{3}}\) (b) \(F=\frac{m v^{2}}{r}\) (c) \(F=\frac{m v^{2}}{r^{2}}\) (d) \(F=\frac{m^{2} v^{2}}{2 r}\)

The dimensions of a rectangular block measured with callipers having least count of \(0.01 \mathrm{~cm}\) are \(5 \mathrm{~mm} \times 10 \mathrm{~mm} \times 5 \mathrm{~mm} .\) The maximum percentage error in the measurement of the volume of the block is (a) \(5 \%\) (b) \(10 \%\) (c) \(15 \%\) (d) 2096

The damping force of an oscillating particle is observed to be proportional to velocity. The constant of proportionality can be measured in (a) \(\mathrm{kg} \mathrm{s}^{-1}\) (b) \(\mathrm{kg} \mathrm{s}\) (c) \(\mathrm{kg} \mathrm{ms}^{-1}\) (d) \(\mathrm{kg} \mathrm{m}^{-1} \mathrm{~s}^{-1}\)

A resistor of \(10 \mathrm{k} \Omega\) having tolerance \(10 \%\) is connected in series with another resistor of \(20 \mathrm{k} \Omega\) having tolerance 20\%. The tolerance of the combination will be approximately (a) 109 (b) \(13 \%\) (c) \(17 \%\) (d) \(20 \%\)

The fundamental unit, which has the same power in the dimensional formulae of surface tension and viscosity is (a) mass (b) length (c) time (d) None of these

A resistor of \(4 \mathrm{k} \Omega\) with tolerance \(10 \%\) is connected in parallel with a resistor of \(6 \mathrm{~kW}\) with tolerance \(100 \%\). The tolerance of the parallel combination is nearly (a) \(10 \%\) (b) \(20 \%\) (c) \(30 \%\) (d) \(40 \%\)

The mass and volume of a body are \(4.237 \mathrm{~g}\) and \(2.5 \mathrm{~cm}^{3}\) respectively. The density of material of the body in correct significant figures is. [NCERT] (a) \(1.6048 \mathrm{~g} \mathrm{~cm}^{-3}\) (b) \(1.69 \mathrm{~g} \mathrm{~cm}^{-3}\) (c) \(1.7 \mathrm{~g} \mathrm{~cm}^{-3}\) (d) \(1.695 \mathrm{~g} \mathrm{~cm}^{-3}\)

The SI unit of length is metre. Suppose we adopt a new unit of length which equal \(x\) metre. The area of \(1 \mathrm{~m}^{2}\) expressed in terms of the new unit has a magnitude (a) \(x\) (b) \(x^{2}\) (c) \(x^{-1}\) (d) \(x^{-2}\)

What is the power of a \(100 \mathrm{~W}\) bulb in CGS units? (a) \(10^{6} \mathrm{ergs}^{-1}\) (b) \(10^{7}\) ergs \(^{-1}\) (c) \(10^{9}\) ergs \(^{-1}\) (d) \(10^{11}\) ergs \(^{-1}\)

Which of the following combinations have the dimensions of time? \(L-C \cdot R\) represents inductance, capacitance and resistance respectively? (a) \(R C\) (b) \(\sqrt{L C}\) (c) \(R / C\) (d) \(C / L\)

Photon is quantum of radiation with energy \(E=h v\) where \(v\) is frequency and \(h\) is Planck's constant. The dimensions of \(h\) are the same as that of [NCERT Exemplar] (a) Linear impulse (b) Angular impulse (c) Linear momentum (d) Angular momentum

SI unit of intensity of wave is (a) \(\mathrm{J} \mathrm{m}^{-2} \mathrm{~s}^{-1}\) (b) \(\mathrm{J} \mathrm{m}^{-1} \mathrm{~s}^{-2}\) (c) \(\mathrm{W} \mathrm{m}^{-2}\) (d) \(\mathrm{J} \mathrm{m}^{-2}\)

Which of the following is a unit of permeability (a) \(\mathrm{H} / \mathrm{m}\) (b) \(\mathrm{Wb} / \mathrm{Am}\) (c) ohm \(\times \mathrm{s} / \mathrm{m}\) (d) \(\mathrm{V} \times \mathrm{s} / \mathrm{m}^{2}\)

A suitable unit for gravitational constant is (a) \(\mathrm{kg}-\mathrm{m} \mathrm{s}^{-1}\) (b) \(\mathrm{Nm}^{-1} \mathrm{~s}\) (c) \(\mathrm{Nm}^{2} \mathrm{~kg}^{-2}\) (d) \(\mathrm{kg} \mathrm{ms}^{-1}\)

If Planck's constant ( \(h\) ) and speed of light in vacuum (c) are taken as two fundamental quantities, which one of the following can, in addition, be taken to express length, mass and time in terms of the three chosen fundamental quantities? \(\quad\) [NCERT Exemplar] (a) Mass of electron \(\left(m_{e}\right)\) (b) Universal gravitational constant \((G)\) (c) Charge of clectron (e) (d) Mass of proton \(\left(m_{p}\right)\)

If \(L\) denotes the inductance of an inductor through which a current \(I\) is flowing, then the dimensional formula of \(L I^{2}\) is (a) \(\left[\mathrm{MLT}^{-2}\right]\) (b) \(\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]\) (c) \(\left[\mathrm{M}^{2} \mathrm{~L}^{2} \mathrm{~T}^{-2}\right]\) (d) not expressible in terms of \(M, L, T\)

One yard in SI unit is equal (a) \(1.9144 \mathrm{~m}\) (b) \(0.9144 \mathrm{~m}\) (c) \(0.09144 \mathrm{~km}\) (d) \(1.0936 \mathrm{~km}\)