## Numerical

In a particular system of units, a physical quantity can be expressed in terms of the electric charge $e$, electron mass $m_{e}$, Planck's constant $h...

An optical bench has 1.5 m long scale having four equal divisions in each cm. While measuring the focal length of a convex lens, the lens is kept at 7...

A steel wire of diameter $$0.5$$ $$mm$$ and Young's modulus $$2 \times {10^{11}}\,\,N{m^{ - 2}}$$ carries a load of mass $$M.$$ The length of the wire...

The energy of a system as a function of time t is given as E(t) = $${A^2}\exp \left( { - \alpha t} \right)$$, where $$\alpha = 0.2\,{s^{ - 1}}$$. The...

During Searle's experiment, zero of the Vernier scale lies between 3.20 $$ \times $$ 10-2 m and 3.25 $$ \times $$ 10-2 m of the
main scale. The 20th d...

To find the distance d over which a signal can be seen clearly in foggy conditions, a railways engineer uses
dimensional analysis and assumes that the...

## MCQ (Single Correct Answer)

Area of the cross-section of a wire is measured using a screw gauge. The pitch of the main scale is $0.5 \mathrm{~mm}$. The circular scale has 100 di...

The smallest division on the main scale of a Vernier calipers is 0.1 cm. Ten divisions of the Vernier scale correspond to nine divisions of the main s...

In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantitie...

In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantitie...

If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is d...

If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is d...

A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the...

There are two Vernier calipers both of which have 1 cm divided into 10 equal divisions on the main scale.
The Vernier scale of one of the calipers (C1...

Match List I with List II and select the correct answer using the codes given below the lists:
List I
P. Boltzmann Constant
Q. Coefficient of viscosit...

The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero
of the Vernier scale lies between 5.10 ...

In the determination of Young's modulus $$\left( {Y = {{4MLg} \over {\pi l{d^2}}}} \right)$$
by using Searle's method, a wire of length L = 2 m
and di...

A dense collection of equal number of electrons and positive ions is called neutral plasma. Certain solids containing
fixed positive ions surrounded b...

A dense collection of equal number of electrons and positive ions is called neutral plasma. Certain solids containing
fixed positive ions surrounded b...

The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with
a screw gauge, whose pitch is 0.5 mm and t...

A vernier calipers has 1 mm marks on the main scale. It has 20 equal divisions on the Vernier scale which match with 16 main scale divisions. For this...

Student I, II and III perform an experiment for measuring the acceleration due to gravity (g) using a
simple pendulum. They use different length of th...

A student performs an experiment to determine the Young's modulus of a wire, exactly 2 m long,
by Searle's method. In a particular reading, the studen...

Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed
are given in Column II. Match the...

A student performs an experiment for determination of $$\mathrm g\left(=\frac{4\mathrm\pi^2\mathcal l}{\mathrm T^2}\right)$$.
The error in length $$\m...

In a screw gauge, the zero of main scale coincides with the fifth division of circular scale in figure (i).The circular division of screw gauge is 50....

Which of the following set have different dimensions?

Pressure depends on distance as, $$P = {\alpha \over \beta }\exp \left( { - {{\alpha z} \over {k\theta }}} \right)$$, where $$\alpha $$, $$\beta $$ a...

A wire of length $$l = 6 \pm 0.06$$ cm and $$r = 0.5 \pm 0.005$$ cm and mass $$m = 0.3 \pm 0.003$$ gm. Maximum percentage error in density is

A cube has a side of length 1.2 ✕ 10-2 m. Calculate its volume.

A quantity X is given by $${\varepsilon _0}L{{\Delta V} \over {\Delta t}}$$ where $${\varepsilon _0}$$ is the permittivity of the free space, L is a l...

The dimension of $$\left( {{1 \over 2}} \right){\varepsilon _0}{E^2}$$
( $${\varepsilon _0}$$ : permittivity of free space, E electric field )

## MCQ (More than One Correct Answer)

A physical quantity $$\overrightarrow S $$ is defined as $$\overrightarrow S = (\overrightarrow E \times \overrightarrow B )/{\mu _0}$$, where $$\ov...

Sometimes it is convenient to construct a system of units so that all quantities can be expressed in
terms of only one physical quantity. In one such ...

Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of L, which of the following statement...

In an experiment to determine the acceleration due to gravity g, the formula used for the time period of a
periodic motion is $$T = 2\pi \sqrt {{{7\le...

A length-scale (l) depends on the permittivity ($$\varepsilon $$) of a dielectric material, Boltzmann constant (kB), the absolute temperature (T), the...

In terms of potential difference V, electric current I, permittivity $${\varepsilon _0}$$, permeability $${\mu _0}$$ and speed of light c,
the dimensi...

Planck's constant h, speed of light c and gravitational constant G are used to form a unit of length L and a
unit of mass M. Then the correct option(s...

Consider a Vernier callipers in which each 1 cm on the main scale is divided into 8 equal divisions and a
screw gauge with 100 divisions on its circul...

A student is performing an experiment using a resonance column and a tuning fork of frequency 244 s$$-$$1. He is told that the air in the tube has bee...

A student uses a simple pendulum of exactly 1m length to determine g, the acceleration due to gravity. He
uses a stop watch with the least count of 1 ...

The SI unit of inductance, the henry can be written as

Let [$${\mathrm\varepsilon}_\mathrm o$$] denote the dimentional formula of the permittivity of the vacuum, and [$$\mu_o$$] that of the permeability of...

The pairs of physical quantities that have the same dimensions is (are):

The dimensions of the quantities in one ( or more ) of the following pairs are the same. Identify the pair(s)

## Subjective

The side of a cube is measured by vernier callipers (10 divisions of a vernier scale coincide with
9 divisions of main scale, where 1 division of main...

A screw gauge having 100 equal divisions and a pitch of length 1 mm is used to measure the diameter of a wire of length 5.6 cm. The main scale reading...

In Searle's experiment, which is used to find Young's Modulus of elasticity, the diameter of experimental wire is D = 0.05 cm ( measured by a scale of...

If nth divisions of the main scale coincide with (n+1)th divisions
of vernier scale. Given one main scale division is equal to 'a' units. Find the
lea...

Column - I gives the three physical quantities. Select the appropriate units for the choices given in Column - II. Some of the physical quantities may...

Match the physical quantities given in column I with dimension expressed in terms of mass (M), length (L), time (T), and charge (Q) given in column II...

Write the dimensions of the followings in terms of mass, time, length and charge
(i) magnetic flux
(ii) rigidity modulus

A gas bubble, from an explosion under water, oscillates with a period T proportional to padbEc. Where 'P' is the static pressure, 'd' is the density o...

Give the MKS units for each of the following quantities.
(i) Young's modulus
(ii) Magnetic Induction
(iii) Power of a lens

## Fill in the Blanks

The equation of state for real gas is given by $$\left( {P + {a \over {{V^2}}}} \right)\left( {V - b} \right) = RT$$. The dimention of the constant a ...

In the formula X = 3YZ2, X and Z have dimensions of capacitance and magnetic induction respectively. The dimensions of Y in MKSQ system are __________...

Plank' constant has dimension __________.