50 MCQs on Units & Measurement – NCERT Class 11 Physics Chapter 1 (JEE/NEET)

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Physics — UNITS AND MEASUREMENT

50 Questions Class 11 MCQs

The physical quantity having the dimension \([M^0 L^1 T^{-1}]\) is:

a a. Velocity b b. Acceleration c c. Force d d. Momentum

The SI unit of luminous intensity is:

a a. Candela b b. Lumen c c. Lux d d. Watt

The SI base unit of temperature is:

a a. Celsius b b. Kelvin c c. Fahrenheit d d. Rankine

Which of the following is not a base quantity in SI?

a a. Length b b. Mass c c. Time d d. Speed

The dimensional formula of force is:

a a. \([M L T^{-2}]\) b b. \([M L^2 T^{-2}]\) c c. \([M L^{-1} T^{-2}]\) d d. \([M^0 L T^{-2}]\)

The dimensional formula of work is:

a a. \([M L T^{-2}]\) b b. \([M L^2 T^{-2}]\) c c. \([M L^2 T^{-1}]\) d d. \([M^0 L^2 T^{-2}]\)

Which of the following is a derived unit?

a a. Metre b b. Kilogram c c. Newton d d. Second

1 femtometre (fm) is equal to:

a a. \(10^{-9}\) m b b. \(10^{-12}\) m c c. \(10^{-15}\) m d d. \(10^{-18}\) m

The unit of power in SI is:

a a. Joule b b. Watt c c. Newton d d. Pascal

The physical quantity having dimensions \([M^0 L T^{-2}]\) is:

a a. Force b b. Pressure c c. Acceleration d d. Surface tension

Which of the following pairs is correctly matched (quantity–unit)?

a a. Energy – watt b b. Power – joule c c. Force – newton d d. Pressure – joule

The SI unit of momentum is:

a a. kg m b b. kg m s\(^{-1}\) c c. N s\(^{-1}\) d d. N m

If \(Q = \frac{A B^2}{C}\), where A, B, C are physical quantities, then the dimensions of Q are:

a a. \([A][B]^2[C]^{-1}\) b b. \([A]^2[B][C]\) c c. \([A][B][C]^2\) d d. \([A]^2[B]^2[C]^{-1}\)

Which of the following is a dimensionless quantity?

a a. Refractive index b b. Work c c. Power d d. Force

The dimensional formula of pressure is:

a a. \([M L^{-1} T^{-2}]\) b b. \([M L^{0} T^{-2}]\) c c. \([M L T^{-2}]\) d d. \([M^0 L^{-1} T^{-2}]\)

Which physical quantity has the same dimensions as torque?

a a. Power b b. Work c c. Momentum d d. Impulse

The dimensional formula of Planck’s constant h is:

a a. \([M L^2 T^{-1}]\) b b. \([M L T^{-1}]\) c c. \([M L^2 T^{-2}]\) d d. \([M^0 L^2 T^{-1}]\)

The dimensional formula of universal gravitational constant G is:

a a. \([M^{-1} L^3 T^{-2}]\) b b. \([M L^{-3} T^{-2}]\) c c. \([M^{-2} L^3 T^{-2}]\) d d. \([M^{-1} L^2 T^{-2}]\)

In the equation \(E = mc^2\), the dimensions of \(c^2\) are:

a a. \([L^2 T^{-2}]\) b b. \([L T^{-2}]\) c c. \([L^2 T^{-1}]\) d d. \([L T^{-1}]\)

Which of the following is a pair of like dimensions?

a a. Impulse and power b b. Force and momentum c c. Work and energy d d. Pressure and energy

A relation \(v = u + at\) is:

a a. Dimensionally correct b b. Dimensionally incorrect c c. Correct only for constant velocity d d. Correct only for large \(t\)

A relation \(x = vt + \frac{1}{2} at^2\) represents displacement. The dimensional formula of the second term is:

a a. \([L]\) b b. \([L T^{-1}]\) c c. \([L T^{-2}]\) d d. \([M L]\)

Which equation is dimensionally inconsistent?

a a. \(s = ut + \frac{1}{2}at^2\) b b. \(v^2 = u^2 + 2as\) c c. \(v = u + at^2\) d d. \(p = mv\)

The dimensions of \(\epsilon_0\) (permittivity of free space) are:

a a. \([M^{-1} L^{-3} T^{4} I^2]\) b b. \([M^{-1} L^{-2} T^{4} I^2]\) c c. \([M^{-2} L^{-3} T^{4} I^2]\) d d. \([M^{-1} L^{-3} T^{-4} I^2]\)

If period \(T\) of a simple pendulum depends on length \(l\) and acceleration due to gravity \(g\), then by dimensional analysis:

a a. \(T \propto l g\) b b. \(T \propto \sqrt{l/g}\) c c. \(T \propto \sqrt{lg}\) d d. \(T \propto g/l\)

The escape velocity \(v\) from a planet of mass \(M\) and radius \(R\) depends on \(G\), \(M\) and \(R\). Dimensional analysis gives:

a a. \(v \propto \sqrt{\frac{GM}{R}}\) b b. \(v \propto \frac{GM}{R^2}\) c c. \(v \propto \sqrt{\frac{G^2 M}{R^3}}\) d d. \(v \propto \frac{G M^2}{R}\)

The time period of a satellite in circular orbit of radius \(r\) around Earth (mass \(M\), gravitational constant \(G\)) is proportional to:

a a. \(\sqrt{\frac{r^3}{GM}}\) b b. \(\sqrt{\frac{GM}{r^3}}\) c c. \(\frac{r^2}{GM}\) d d. \(\sqrt{\frac{r}{GM}}\)

The quantity which does not have dimensions of \([M L^2 T^{-2}]\) is:

a a. Work b b. Energy c c. Torque d d. Power

The range \(R\) of a projectile is given by \(R = \frac{u^2 \sin 2\theta}{g}\). Dimensional analysis can show that:

a a. \(R\) is proportional to \(u^2/g\) b b. \(R\) is proportional to \(\sin 2\theta\) c c. Exact factor \(\sin 2\theta\) must appear d d. \(R\) is independent of \(g\)

The dimensions of angular momentum are:

a a. \([M L^2 T^{-1}]\) b b. \([M L T^{-1}]\) c c. \([M L^2 T^{-2}]\) d d. \([M L T^{-2}]\)

Which of the following equations is dimensionally correct?

a a. \(E = \frac{1}{2}mv^3\) b b. \(E = \frac{1}{2}mv^2\) c c. \(E = \frac{1}{2}m^2v\) d d. \(E = mgv\)

The dimensional formula of coefficient of viscosity \(\eta\) is:

a a. \([M L^{-1} T^{-1}]\) b b. \([M L^{-1} T^{-2}]\) c c. \([M L T^{-1}]\) d d. \([M^0 L^0 T^{-1}]\)

The dimensions of surface tension are:

a a. \([M T^{-2}]\) b b. \([M L^{-1} T^{-2}]\) c c. \([M L T^{-2}]\) d d. \([M L^{-2} T^{-2}]\)

The physical quantity having dimensions \([M^0 L^0 T^0]\) is:

a a. Angle in radians b b. Energy c c. Force d d. Velocity

Which one of the following sets contains only dimensionless quantities?

a a. Refractive index, strain, angle b b. Strain, stress, refractive index c c. Angle, velocity, strain d d. Refractive index, stress, angle

The order of magnitude of \(4.6 \times 10^3\) is:

a a. \(10^2\) b b. \(10^3\) c c. \(10^4\) d d. \(10^5\)

The quantity which has different dimensions from the others is:

a a. Energy per unit volume b b. Pressure c c. Stress d d. Force per unit length

The dimensional formula of electric charge is:

a a. \([I T]\) b b. \([M L T^{-1}]\) c c. \([M^0 L^0 T^0]\) d d. \([I^2 T]\)

Which one is not a correct pair (quantity–unit)?

a a. Magnetic field – tesla b b. Frequency – hertz c c. Energy – electron volt d d. Power – newton

Dimensional analysis cannot be used to:

a a. Check dimensional correctness of an equation b b. Predict form of a physical relation up to a constant c c. Derive relation between quantities d d. Find numerical value of a dimensionless constant

If density \(\rho\) has dimensions \([M L^{-3}]\) and speed \(v\) has \([L T^{-1}]\), then \(\rho v^2\) has dimension of:

a a. Pressure b b. Force c c. Energy d d. Power

The dimensions of \(\frac{h^2}{2mL^2}\) (appearing in quantum mechanics) are:

a a. Energy b b. Momentum c c. Force d d. Power

The dimension of Boltzmann constant \(k_B\) in \(E = k_B T\) is:

a a. \([M L^2 T^{-2} K^{-1}]\) b b. \([M L^2 T^{-2}]\) c c. \([M L T^{-2}]\) d d. \([M^0 L^0 T^0 K^{-1}]\)

If force \(F\) depends on charge \(q\), velocity \(v\) and magnetic field \(B\) as \(F \propto q^a v^b B^c\), using dimensional analysis, exponents are:

a a. \(a = 1, b = 1, c = 1\) b b. \(a = 1, b = 0, c = 1\) c c. \(a = 0, b = 1, c = 1\) d d. \(a = 1, b = 1, c = 0\)

The Reynolds number \(\text{Re}\) for flow of a fluid in a pipe is defined as \(\text{Re} = \frac{\rho v D}{\eta}\), where \(\rho\) is density, \(v\) velocity, \(D\) diameter, \(\eta\) viscosity. Its dimensions are:

a a. \([M^0 L^0 T^0]\) b b. \([M L^{-1} T^{-1}]\) c c. \([M^0 L T^{-1}]\) d d. \([M L T^{-1}]\)

The Mach number is defined as the ratio of the speed of an object to the speed of sound. Its dimensions are:

a a. \([L T^{-1}]\) b b. \([M^0 L^0 T^0]\) c c. \([T^{-1}]\) d d. \([L^2 T^{-2}]\)

Planck length \(l_p\) is constructed from fundamental constants \(G\), \(\hbar\) and \(c\). Its dimensional form is \(l_p \propto G^a \hbar^b c^c\). Matching dimensions of length gives:

a a. \(a = \frac{1}{2}, b = \frac{1}{2}, c = -\frac{3}{2}\) b b. \(a = 1, b = 1, c = -2\) c c. \(a = \frac{1}{3}, b = \frac{1}{3}, c = -\frac{1}{3}\) d d. \(a = \frac{2}{3}, b = \frac{1}{3}, c = -1\)

The dimension of permeability of free space \(\mu_0\) in SI is:

a a. \([M L T^{-2} I^{-2}]\) b b. \([M L T^{-1} I^{-2}]\) c c. \([M L T^{-2} I^{-1}]\) d d. \([M^0 L^0 T^0 I^{-2}]\)

The Stefan–Boltzmann constant \(\sigma\) in \(P = \sigma A T^4\) has dimensions:

a a. \([M T^{-3} K^{-4}]\) b b. \([M L^2 T^{-3} K^{-4}]\) c c. \([M L^{-2} T^{-3} K^{-4}]\) d d. \([M L^0 T^{-3} K^{-4}]\)

The Avogadro number \(N_A\) appears in \(n = \frac{N}{N_A}\) where \(n\) is amount of substance, \(N\) number of molecules. The dimensions of \(N_A\) are:

a a. \([M^0 L^0 T^0]\) b b. \([mol^{-1}]\) c c. \([L^{-3}]\) d d. \([T^{-1}]\)

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Frequently Asked Questions

A physical quantity is a property of a system that can be measured and expressed numerically with a unit, such as length, mass, and time.?

A unit is a standard reference chosen to measure a physical quantity, e.g., metre for length, kilogram for mass.?

Physical quantities that are independent of other quantities, e.g., length, mass, time, electric current, temperature, amount of substance, luminous intensity.?

There are seven SI base quantities: length, mass, time, electric current, thermodynamic temperature, amount of substance, luminous intensity.?

Metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), candela (cd).?

Quantities defined using base quantities (e.g., velocity, force); their units are combinations of base units (e.g., \(m\ s^{-1},\ kg\ m\ s^{-2}\).?

SI supplementary units are: radian (rad) for plane angle and steradian (sr) for solid angle.?

It is internationally accepted, coherent, and based on seven base units with well-defined standards, simplifying scientific communication.?

A system where derived units are obtained from base units without additional numerical factors, e.g., \(1\ N = 1\ kg\ m\ s^{-2}\).?

It is the expression of a physical quantity in terms of base dimensions, like \([M^aL^bT^c]\) for mass, length, and time powers.?

Velocity has dimensional formula \([LT^{-1}]\).?

Force has dimensional formula \([MLT^{-2}]\).?

In a physically meaningful equation, the dimensions of all terms on both sides must be the same.?

To check the dimensional consistency of equations, derive relations between quantities, and convert from one system of units to another.?

It cannot determine dimensionless constants (like 1/2, 2p), and it fails if quantities of different dimensions are added.?

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Physics — UNITS AND MEASUREMENT

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Frequently Asked Questions

Q 01 What is a physical quantity?

Q 02 What is a unit?

Q 03 What are fundamental (base) quantities?

Q 04 How many SI base quantities are there?

Q 05 What are the SI base units?

Q 06 What are derived quantities and units?

Q 07 What are supplementary units in SI?

Q 08 Why is the SI system preferred?

Q 09 What is meant by “coherent system of units”?

Q 10 What is dimensional formula?

Q 11 What is the dimensional formula of velocity?

Q 12 What is the dimensional formula of force?

Q 13 State the principle of homogeneity of dimensions.

Q 14 What are the uses of dimensional analysis?

Q 15 Give one limitation of dimensional analysis.

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