Derive an expression for the period of motion of a simple pendulum. On which factors does it depend?

Concept: Periodic and Oscillatory Motions

A ballet dancer spins about a vertical axis at 2.5Π rad/s with his both arms outstretched. With the arms folded, the moment of inertia about the same axis of rotation changes by 25%. Calculate the new speed of rotation in r.p.m.

Concept: Physical Significance of M.I (Moment of Inertia)

Discuss different modes of vibrations in an air column of a pipe open at both the ends.

Concept: Study of Vibrations of Air Columns

Draw neat labelled diagrams for modes of vibration of an air column in a pipe when it is closed at one end.

Hence derive an expression for fundamental frequency in each case.

Concept: Study of Vibrations of Air Columns

A soap bubble of radius 12 cm is blown. Surface tension of soap solution is 30 dyne/cm. Calculate the work done in blowing the soap bubble.

Concept: Capillarity and Capillary Action

In a conical pendulum, a string of length 120 cm is fixed at rigid support and carries a mass

of 150 g at its free end. If the mass is revolved in a horizontal circle of radius 0.2 m around a

vertical axis, calculate tension in the string (g = 9.8 m/s^{2})

Concept: Surface Tension

Discuss the behaviour of wire under increasing load.

Concept: Definition of Stress and Strain

Derive an expression for one dimensional simple harmonic progressive wave travelling in the

direction of positive X-axis. Express it in ‘two’ different forms.

Concept: Simple Harmonic Progressive Waves,

The kinetic energy of nitrogen per unit mass at 300 K is 2.5 × 106 J/kg. Find the kinetic energy of 4 kg oxygen at 600 K. (Molecular weight of nitrogen = 28, Molecular weight of oxygen = 32)

Concept: K.E.(Kinetic Energy) and P.E.(Potential Energy) in S.H.M.

A racing car completes 5 rounds of a circular track in 2 minutes. Find the radius of the track

if the car has uniform centripetal acceleration of Π^{2} m/s^{2}.

Concept: Dynamics of Uniform Circular Motion - Centripetal Force

A body weighs 4.0 kg-wt on the surface of the Earth. What will be its weight on the surface of a plant whose mass is `1/8` th of the mass of the Earth and radius half `(1/2)` of that of the Earth?

Concept: Surface Tension

Define radius of gyration

Concept: Physical Significance of M.I (Moment of Inertia)

Explain the physical significance of radius of gyration

Concept: Physical Significance of M.I (Moment of Inertia)

A body of mass 1 kg is made to oscillate on a spring of force constant 16 N/m. Calculate:

a) Angular frequency

b) frequency of vibration.

Concept: Simple Harmonic Motion

Show that the surface tension of a liquid is numerically equal to the surface energy per unit

area.

Concept: Surface Tension

Show graphical representation of energy distribution spectrum of perfectly black body.

Concept: Qualitative Ideas of Blackbody Radiation

Explain black body radiation spectrum in terms of wavelength

Concept: Qualitative Ideas of Blackbody Radiation

‘g’ is the acceleration due to gravity on the surface of the Earth and ‘R’ is the radius of the

Earth.

Show that acceleration due to gravity at height ‘h’ above the surface of the Earth is

`gh = g (R/(R+H))^2`

Concept: Acceleration Due to Gravity and Its Variation with Altitude and Depth

In Melde’s experiment, the number of loops on a string changes from 7 to 5 by the addition of 0.015 kgwt. Find the initial tension applied to the string.

Concept: Formation of Stationary Waves on String

A planet is revolving around a star in a circular orbit of radius R with a period T. If the

gravitational force between the planet and the star is proportional to `R^(-3/2)` then

A) `T^2 prop R^(5/2)`

B) `T^2 prop R^((-7)/2)`

C) `T^2 prop R^(3/2)`

D) `T^2 prop R^4`

Concept: Vertical Circular Motion Due to Earth’s Gravitation

If ‘L’ is the angular momentum and ‘I’ is the moment of inertia of a rotating body, then `L^2/(2I)`represents its _____

(A) rotational P.E.

(B) total energy

(C) rotational K.E.

(D) translational K.E

Concept: Definition of M.I., K.E. of Rotating Body

A particle executing linear S.H.M. has velocities v_{1} and v2 at distances x_{1} and x_{2} respectively from the mean position. The angular velocity of the particle is _______

A) `sqrt((x_1^2 - x_2^2)/(v_2^2 - v_1^2))`

B) `sqrt((v_2^2 - v_1^2)/(x_1^2 - x_2^2))`

C) `sqrt((x_1^2 + x_2^2)/(v_2^2 + v_1^2))`

D) `sqrt((v_2^2 + v_1^2)/(x_2^2 + x_1^2))`

Concept: Differential Equation of Linear S.H.M.

A metal rod having coefficient of linear expansion (α) and Young’s modulus (Y) is heated to

raise the temperature by ΔΘ. The stress exerted by the rod is _______

A) `(Yα)/(ΔΘ)`

B) `(YΔΘ)/α`

C) YαΔΘ

D) `(αΔΘ)/Y`

Concept: Definition of Stress and Strain

A big drop of radius R is formed from 1000 droplets of water. The radius of a droplet will be _______

A) 10 R

B) R/10

C) R/100

D) R/1000

Concept: Surface Tension

Apparent frequency of the sound heard by a listener is less than the actual frequency of sound emitted by source. In this case _______.

(A) listener moves towards source

(B) source moves towards listener

(C) listener moves away from the source.

(D) source and listener move towards each other.

Concept: Beats

The substance which allows heat radiations to pass through is _______.

(A) iron

(B) water vapour

(C) wood

(D) dry air

Concept: Temperature and Heat

Obtain an expression for the induced e.m.f. in a coil rotating with uniform angular velocity in

uniform magnetic field. Plot a graph of variation of induced e.m.f. against phase (Θ = ωt) over one cycle.

Concept: Magnetic Properties of Materials

The energy density at a point in a medium of dielectric constant 6 is 26.55 × 10^{6} J/m^{3}. Calculate electric field intensity at that point. (ε_{0} = 8.85 × 10^{−12} SI units).

Concept: Energy Density of a Medium

Write notes on Nuclear fission

Concept: Nuclear Energy - Nuclear Fusion – Energy Generation in Stars

Write notes on Nuclear fusion

Concept: Nuclear Energy - Nuclear Fusion – Energy Generation in Stars

A galvanometer has a resistance of 16Ω. It shows full scale deflection, when a current of 20 mA is passed through it. The only shunt resistance available is 0.06 which is not appropriate to convert a galvanometer into an ammeter. How much resistance should be connected in series with the coil of galvanometer, so that the range of ammeter is 8 A?

Concept: Moving Coil Galvanometer

Draw a well labelled diagram of photoelectric cell.

Concept: Particle Nature of Light

Explain the observations made by Hertz and Lenard about the phenomenon of photoelectric

emission.

Concept: Particle Nature of Light

Explain the working of transistor as a switch.

Concept: Transistor as a Switch

The refractive indices of water for red and violet colours are 1.325 and 1.334 respectively.

Find the difference between the velocities of rays for these two colours in water. (c = 3 × 10^{8} m/s)

Concept: Polarisation

In Young’s experiment, the ratio of intensity at the maxima and minima in an interference

pattern is 36 : 9. What will be the ratio of the intensities of two interfering waves?

Concept: Interference of Light Waves and Young’S Experiment

Explain the principle of potentiometer.

Concept: Meter Bridge

Define Magnetic intensity.

Concept: Magnetisation and Magnetic Intensity

What do you mean by polar molecules and non-polar molecules? Give ‘one’ example each.

Concept: Atomic Masses and Composition of Nucleus

The minimum angular separation between two stars is 4 × 10^{−6} rad, if telescope is used to observe them with an objective of aperture 16 cm. Find the wavelength of light used.

Concept: Wave Theory of Light

Explain the need for modulation related to the size of antenna (aerial).

Concept: Modulation and Its Necessity

Four resistances 4Ω,8Ω,XΩ, and 6Ω are connected in a series so as to form Wheatstone’s

network. If the network is balanced, find the value of ‘X’.

Concept: Wheatstone Bridge

The magnetic susceptibility of annealed iron at saturation is 4224. Find the permeability of

annealed iron at saturation. (μ_{0} = 4Π × 10^{−7} SI unit)

Concept: Magnetic Properties of Materials

A ray of light passes from a vacuum to a medium of refractive index (μ). The angle of

incidence is found to be twice the angle of refraction. The angle of incidence is _______.

A) `cos^(-1)(mu/2)`

B) cos^{−1}(μ)

C) `2 cos^(-1) (mu/2)`

D) `2 sin^(-1) (mu/2)`

Concept: Polarisation

The fringes produced in diffraction pattern are of _______.

(A) equal width with same intensity

(B) unequal width with varying intensity

(C) equal intensity\

(D) equal width with varying intensity

Concept: Interference of Light Waves and Young’S Experiment

If ‘R’ is the radius of dees and ‘B’ be the magnetic field of induction in which positive charges (q) of mass (m) escape from the cyclotron, then its maximum speed (vmax) is _______.

A) `(qR)/(Bm)`

B)`(qm)/(Br)`

C) `(qBR)/m`

D) `m/(qBR)`

Concept: Electromagnetic Induction

The number of photoelectrons emitted _______.

(A) varies inversely with frequency

(B) varies directly with frequency

(C) varies inversely with intensity

(D) varies directly with intensity

Concept: Particle Nature of Light

The width of depletion region of p-n junction diode is _______.

(A) 0.5 nm to 1 nm

(B) 5 nm to 10 nm

(C) 50 nm to 500 nm

(D) 500 nm to 1000 nm

Concept: Special Purpose P-n Junction Diodes

Any device that converts one form of energy into another is termed as ______.

(A) amplifier

(B) transducer

(C) receiver

(D) demodulator

Concept: Elements of a Communication System

A transformer converts 240 V AC to 60 V AC. The secondary has 75 turns. The number of turns in primary are _______.

(A) 600

(B) 500

(C) 400

(D) 300

Concept: Transformers