Write the rules for determining significant figures.

Explain what is meant by Cartesian coordinate system?

A particle has its position moved from \(\overset { \rightarrow }{ { r }_{ 1 } } =3\hat { i } +4\hat { j } \) to \(\overset { \rightarrow }{ { r }_{ 2 } } =\hat { i } +2\hat { j } \) Calculate the displacement vector (\(\Delta \)\(\overrightarrow { r } \)) and draw the \(\overrightarrow { { r }_{ 1 } } \), \(\overrightarrow { { r }_{ 2 } } \) and \(\Delta \overrightarrow { r } \) vector in a two dimensional cartesian coordinate system.

If the position vector of the particle is given by \(\vec { r } ={ 3t }^{ 2 }\hat { i } +5t\hat { j } +4\hat { k } \), Find the
(a) The velocity of the particle at t = 3 s
(b) Speed of the particle at t = 3 s
(c) Acceleration of the particle at time t = 3s

The position vector of a particle is given by \(\vec { r } =3t\hat { i } +5t^{ 2 }\hat { j } +7\hat { k } \). Find the direction in which the particle experiences net force?

Consider an object of mass 50 kg at rest on the floor. A Force of 5 N is applied on the object but it does not move. What is the frictional force that acts on the object?

Explain the characteristics of elastic and inelastic collision.

Define torque and mention its unit.

Four round objects namely a ring, a disc, a hollow sphere and a solid sphere with same radius R start to roll down an incline at the same time. Find out which object will reach the bottom first.

If the Earth has no tilt, what happens to the seasons of the Earth?

Within the elastic limit, the stretching strain produced in wires A, B, and C due to stress is shown in the figure. Assume the load applied are the same and discuss the elastic property of the material.

Write down the elastic modulus in ascending order

State Pascal’s law in fluids.

a. ‘A lake has more rain’.
b. ‘A hot cup of coff ee has more heat’.
What is wrong in these two statements?

Eiffel tower is made up of iron and its height is roughly 300 m. During winter season (January) in France the temperature is 2°C and in hot summer its average temperature 25°C. Calculate the change in height of Eiffel tower between summer and winter. The linear thermal expansion coefficient for iron α = 10 x 10^-6 per °C.

500 g of water is heated from 30°C to 60°C. Ignoring the slight expansion of water, calculate the change in internal energy of the water? (specific heat of water 4184 J/kg.K)

Can we measure the temperature of the object by touching it?

In an adiabatic expansion of the air, the volume is increased by 4%, what is percentage change in pressure?
(For air \(\gamma \) = 1.4)

Suppose a person wants to increase the efficiency of the reversible heat engine that is operating between 100°C and 300°C. He had two ways to increase the efficiency. (a) By decreasing the cold reservoir temperature from 100°C to 50°C and keeping the hot reservoir temperature constant (b) by increasing the temperature of the hot reservoir from 300°C to 350°C by keeping the cold reservoir temperature constant. Which is the suitable method?

Which of the following functions of time represent periodic and non-periodic motion?
a. sin ωt + cos ωt
b. ln ωt

Show that for a particle executing simple harmonic motion
a. the average value of kinetic energy is equal to the average value of potential energy.
b. average potential energy = average kinetic energy = \(\frac{1}{2}\) (total energy)
Hint: average kinetic energy =< kinetic energy > = \(\frac{1}{T} \int_{0}^{T}\)(Kineticenergy) dt and
average Potential energy = < Potential energy > = \(\frac{1}{T} \int_{0}^{T}\) (Potential energy) dt

A force \(\vec { F } =(6\hat { i } -8\hat { j } +10\hat { k } )\) N produces acceleration of 1 m/s² in a body. Calculate the mass of the body.

Wheels are made circular. Why?

Three blocks of masses 10 kg, 7 kg and 2 kg are placed in contact with each other on a frictionless table. A force of 50 N is applied on the heaviest mass. What is the acceleration of the system?

Which law of motion is involved in rocket propulsion?

A car starts from rest and moves on a surface with uniform acceleration. Draw the graph of kinetic energy versus displacement. What information you can get from that graph?

A light body and a heavy body have the same linear momentum. Which one has greater K.E?

Define power.

A labourer standing near the top of an old wooden step ladder feels unstable. Why?

If the K.E of a satellite revolving around the earth in any orbit is doubled then what will happen to satellite?

Whistle of approaching railway engine is shriller than the receding engine. Give reason