If humans were to settle on other planets, which of the fundamental quantities will be in trouble? Why?

Calculate the angle of
(i) 1⁰ (degree)
(ii) 1' (minute of arc or arc min) and
(iii) 1" (second of arc or arc second) in radians. Use 360⁰ = 2\(\pi\) rad, 1⁰ =6⁰ and 1' = 60"

Arrive at Einstein's mass-energy relation by dimensional method (E = mc²).

Convert
G = 6.67\(\times\)10^-11 N m²kg^-2 to cm³g^-1s^-2

Define displacement and distance.

Write down the kinematic equations for angular motion.

Find the distance travelled by the particle during the time t = 0 to t = 3 seconds from the figure.

What are positive and negative acceleration in straight line motion?

State Newton's third law.

The force that should be applied a body of mass 20 kg. It moves upward with an acceleration of 4 ms^-2. Find the force in the vacuum.

The motion of a particle of mass m is described by h = ut + 1/2 gt². Find the force acting on particle.

A block of mass m is pushed momentarily along a horizontal surface with an initial velocity u. If u_k is the coefficient of kinetic friction between the object and surface, find the time at which the block comes to rest.

A body of mass 5 kg initially at rest is subjected to a force of 20N: What is the kinetic energy acquired by the body at the end of 10s?

An object of mass 2 kg is taken to a height 5 m from the ground (g = 10 ms^-2).
(a) Calculate the potential energy stored in the object.
(b) Where does this potential energy come from?
(c) What external force must act to bring the mass to that height?
(d) What is the net force that acts on the object while the object is taken to the height 'h'?

Show that the work done by the conservative force is independent of the path. Consider the following cases

A pump on the ground floor of a building can pump up water to fill a tank of volume 30 m³ in 15 min. If the tank is 40 m above the ground, how much electric power is consumed by the pump. The efficiency of the pump is 30%.

Define centre of gravity.

Mention any two physical significance of moment of inertia?

Two particles mass 100 g and 300 g at a given time have velocities \(10\hat{i}-7\hat{j}-3\hat{k}\) and \(7\hat{i}-9\hat{j}+6\hat{k}\) ms^-1 respectively. Determine velocity of center of mass.

A metre stick is balanced on a knife edge at its centre. When two coins, each of mass 5g are put one on top of the other at the 12.0 cm mark, the stick is found to be balanced at 45.0 cm, what is the mass of the meter stick?

A student was asked a question ‘why are there summer and winter for us? He replied as since Earth is orbiting in an elliptical orbit, when the Earth is very far away from the Sun(aphelion) there will be winter, when the Earth is nearer to the Sun(perihelion) there will be winter. Is this answer correct? If not, what is the correct explanation for the occurrence of summer and winter?

The following photographs are taken from the recent lunar eclipse which occurred on January 31, 2018. Is it possible to prove that Earth is a sphere from these photographs?

Why the gravitational force between the Earth and the Sun is so great while the same force between two small objects is negligible?

Find the period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle which moves without friction down an inclined plane of indentation \(\alpha\).

A cube of wood floating in water supports a 300 g mass at the centre of its top face. When the mass is removed, the cube rises by 3 cm. Determine the volume of the cube.

Water rises in a capillary tube to a height of 2.0cm. How much will the water rise through another capillary tube whose radius is one-third of the first tube?

Write any three applications of viscosity.

Explain why:
(a) a body with large reflectivity is a poor emitter.
(b) a brass tumbler feels much colder than wooden tray on a chilly day.

A 0.5 mole of gas at temperature 300 K expands isothermally from an initial volume of 2 L to 6 L
(a) What is the work done by the gas?
(b) Estimate the heat added to the gas?
(c) What is the final pressure of the gas?
(The value of gas constant, R = 8.31 J mol^-1 K^-1)

During a cyclic process, a heat engine absorbs 500 J of heat from a hot reservoir, does work and ejects an amount of heat 300 J into the surroundings (cold reservoir). Calculate the efficiency of the heat engine?

Write the equation of state for an ideal gas.

From an equilibrium state A to another equilibrium state A to another equilibrium state B an amount of work equal to 300 J is done on the system. If the gas is taken from state Ato B via a process in which the net heat observed by the system is 10 cal, how much is the net work done by the system in the later case? [Take 1 cal = 4.2 J]

Describe the total degrees of freedom for monoatomic molecule, diatomic molecule and triatomic molecule.

Derive the expression for mean free path of the gas.

State and explain Charle's law.

Explain how does a gas exert pressure on the bases of kinetic theory of gases.

A spring balance has a scale which ranges from 0 to 25 kg and the length of the scale is 0.25m. It is taken to an unknown planet X where the acceleration due to gravity is 11.5 m s⁻¹. Suppose a body of mass M kg is suspended in this spring and made to oscillate with a period of 0.50 s. Compute the gravitational force acting on the body.

Write down the kinetic energy and total energy expressions in terms of linear momentum, For one-dimensional case.

The maximum acceleration of a simple harmonic oscillator is Q_o and the maximum velocity is V_o. What is the displacement amplitude?

Derive the expression for resultant spring constant when two springs having constant k₁ and k₂ are connected in parallel.

Two vibrating tuning forks produce waves whose equation is given by y₁ = 5 sin(240\(\pi\)t) and y₂ = 4 sin(244πt). Compute the number of beats per second.

The sound level from a musical instrument playing is 50 dB. If three identical musical instruments are played together then compute the total intensity. The intensity of the sound from each instrument is 10^-12 W m^-2.

Write the characteristics of wave motion.

Distinguish between transverse and longitudinal waves.