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.

Define angular momentum and derive the expression of it.

Write an expression for the kinetic energy of a body in pure rolling.

The 747 boing plane is landing at a speed of 70 m S^-1 Before touching the ground, the wheels are not rotating. How long a skid mark do the wing wheels leave (assume their mass is 100 kg which is distributed uniformly, radius is 0.7 m, and the coefficient of friction with the ground is 0.5)?

A fly wheel rotates with a uniform angular acceleration. If its angular velocity increases from 20\(\pi\) rad/s to 40\(\pi\) rad/s in 10 seconds. Find the number of rotations in that period.

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).

A car of mass 1200 kg is travelling around a circular path of radius 300 m with a constant speed of 54 km/h. Calculate its angular momentum.

A hoop of radius 2m weights 100 kg. It rolls along a horizontal floor so that its centre of mass has speed of 20 cm/s. How much work has to be done to stop it?

Explain the principle of moments of rotational equilibrium? Hence define mechanical advantage?

Derive the relation between rotational KE and angular momentum.

Derive an expression for center of mass for distributed point masses.

Discuss how the rolling is the combination of translational and rotational and also be possibilities of velocity of different points in pure rolling.

A particle of mass (m) is moving with constant velocity (v). Show that its angular momentum about any point remains constant throughout the motion.

A solid sphere is undergoing pure rolling. What is the ratio of its translational kinetic energy to rotational kinetic energy?

Three particles of masses m₁= 1kg, m₂ = 2kg and m₃ = 3kg are placed at the comers of an equilateral triangle of side 1m as shown in Figure. Find the position of center of mass.

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.

A massless right tangled triangle is suspended with its right angle corner. A mass of 100 kg is suspended from another corner B which subtends an angle \(53^{0}\). Find the mass m that should be suspended from other corner C so that BC (hypotenuse) remains horizontal. 

Discuss the important features of the law of gravitation.

Explain how Newton verified his law of gravitation.

Derive the expression for gravitational potential energy.

Explain in detail the idea of weightlessness using lift as an example.

Derive an expression for escape speed.

Explain the variation of g with altitude.

Derive the time period of satellite orbiting the Earth.

Derive an expression for energy of satellite.

Explain in detail the geostationary and polar satellites.

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?