(i) Explain the use of screw gauge and vernier caliper in measuring smaller distances.
(ii) Write a note on triangulation method and radar method to measure larger distances

Explain propagation of errors in the difference of two quantities and also in the division of two quantities.

Check the correctness of the equation\(\frac { 1 }{ 2 } \)mv² = mgh using dimensional analysis method.

Explain the principle of homogeniety of dimensions. What are its uses? Give example

Discuss the properties of scalar and vector products.

Derive the expression for centripetal acceleration.

Explain the subtraction of vectors.

Two particles move along x axis. The position of particle is given by x = 6.0 t² + 4.0 t + 2.0, acceleration of particle 2 is given by a = -6.0 t and t =0, its velocity is 30 m/s, When the velocities of the particles match, find their velocities.

Two vectors \(\vec A\) and \(\vec B\) of magnitude 5 units and 7 units respectively make an angle 60° with each other as shown below. Find the magnitude of the resultant vector and its direction with respect to 7 unit the vector \(\vec A\).

What are concurrent forces? State Lami's theorem.

Briefly explain 'centrifugal force' with suitable examples.

Describe the method of measuring angle of repose.

How will you confirm Newton's third law by the way of two Bodies in Contact on a Horizontal Surface?

A block of mass m slides down the plane inclined at an angle 60° with an acceleration \(\frac { g }{ 2 } \). Find the coefficient of kinetic friction.

Arrive at an expression for power and velocity. Give some examples for the same.

What is inelastic collision? In which way it is different from elastic collision. Mention few examples in day to day life for inelastic collision.

Deduce the relation between momentum and kinetic energy.

If a particle elastically collides obliquely with a particle of same mass at rest then show that they move perpendicular to each other after collision.

Explain the types of equilibrium with suitable examples?

Derive the expression for moment of inertia of a rod about its center and perpendicular to the rod?

State and prove parallel axis theorem.

Derive an expression for the Center of Mass of Two Point Masses.

A spherical solid ball of 1 kg mass and radius 3 cm is rotating about an axis passing through its centre with an angular velocity of 50 rad/s. Calculate the kinetic energy of rotation.

On the edge of a wall, we build a brick tower that only holds because of the bricks own weight. Our goal is to build a stable 1 tower whose overhang d is greater than the length l of a single brick. What is the minimum number of bricks you need?

A uniform disc of mass 100g has a diameter of 10 cm, Calculate the total energy of the disc when rolling along a horizontal table with a velocity of 20 cms^-1. (take the surface of table as reference).

Write an expression for the KE of a body rolling without slipping with centre of mass as reference.

A solid cylinder when dropped from a height of 2 m acquires a velocity while reaching the ground. If the same cylinder is rolled down from the top of an inclined plane to reach the ground with same velocity, what must be the height of the inclined plane? Also compute the velocity.

Discuss the important features of the law of gravitation.

Explain how Newton arrived at his law of gravitation from Kepler’s third law.

Derive the time period of satellite orbiting the Earth.

Explain the different types of modulus of elasticity?

State and prove Archimedes principle.

What is capillarity? Obtain an expression for the surface tension of a liquid by capillary rise method.

Write the applications of surface tension?

Calculate the volume of one mole of any gas at STP and at room temperature (300K) with the same pressure 1 atm.

A hot water cools from 92°C to 84°C in 3 minutes when the room temperature is 27°C. How long will it take for it to cool from 65°C to 60°C?

Explain in detail the thermal expansion.

Discuss various modes of heat transfer.

What is meant by coefficient of linear expansion superficial & cubical expansion?

Find the adiabatic exponent \(\gamma\) for mixture of μ₁ moles of monoatomic gas and μ₂ moles of a diatomic gas at normal temperature (27°C).

Speed of an atom in an argon gas cylinder equal to the rms speed of a helium gas atom at -20°C? [Atomic mass of Ar =39.90, He =4.04]

Show that for a simple harmonic motion, the phase difference between 
a. displacement and velocity is \(\frac{\pi}{2}\) radian or 90°.
b. velocity and acceleration is  \(\frac{\pi}{2}\) radian or 90°.
c. displacement and acceleration is \(\pi\)  radian or 180°.

Calculate the equivalent spring constant for the following systems and also compute if all the spring constants are equal:

Discuss in detail the energy in simple harmonic motion.

Show that the projection of uniform circular motion on a diameter is SHM.

A simple pendulum has time period T, the point of suspension is now moved upward acceleration to the relation Y= kt² (k = 1 ms^-2) where Y is the verticle displacement the time period now becomes T₂. What is the ratio \(\frac { { T }_{ 1 }^{ 2 } }{ { T }_{ 2 }^{ 2 } } \)? Given g=10 ms^-2.

Consider a string in a guitar whose length is 80 cm and a mass of 0.32 g with tension 80 N is plucked. Compute the first four lowest frequencies produced when it is plucked.

Briefly explain the concept of superposition principle.

Write the applications of reflection of sound waves.

For the travelling : harmonic wave y(x, t) = 2.0 cos 2π [St - 0.0060x + 0.27], where x and yare in cm and t in s.
Calculate the phase difference between oscillatory motion of two points separated by a distance of,
(a) 300 cm
(b) 0.75 m (c)\(\lambda\over 4\)