The expression for rigid body’s “rotational kinetic energy” is 

SOLUTION:

A body undergoing a rotational dynamics with angular velocity ω will also poses a translational motion. Let the velocity for translation motion be ‘’v’’.

We know for translational motion the energy poses by body is kinetic and given as

Also we know that for a body obeying rotation  

v=rω

Substituting in translation

Also there is a relation for moment of inertia i.e 

Substituting we get,

1. Carnivorous animals such as lion and tiger have sharp teeth and powerful jaws to kill prey.
2. Baleen whales are also predators. They hunt krill using their baleen plates as filter-feeding systems.
3. Animals such as chameleons and some frogs have long sticky tongues to catch prey.
4. Most carnivores are usually fast as they need to chase and tire their prey.
5. Some carnivorous animals like snakes and spiders use venom to kill their prey.
6. Carnivores do not have the ability to detoxify vitamin A in the liver.
7. The length of the intestine in the carnivorous animals is small.

Since water is one of the most important compounds needed for various important life processes, a loss of water by transpiration is obviously harmful. This harmful effect becomes dangerous when excessive transpiration leads to the wilting of the plants.Besides wilting, other harmful effects of excessive transpiration include inhibition of protein synthesis and breakdown of proteins and retardation of metabolic processes like photosynthesis. This is the reason why transpiration is often called as a necessary evil.

Born Haber process or more commonly referred to as Born Haber cycle is a method that allows us to observe and analyze energies in a reaction. It mainly helps in describing the formation of ionic compounds from different elements. The methodology further enables us to understand the overall reaction process through a series of steps.

Born-Haber cycle was introduced in the year 1919 by German scientists named Fritz Haber and Max Born. Born Haber cycle is mainly used to calculate the lattice energy. It also involves several steps or processes such as electron affinity, ionization energy, sublimation energy, the heat of formation and dissociation energy

The best time to water flowers is in the morning between the hours of 6-10 a.m. The cooler weather reduces evaporation and helps the water stay where you need it – with the plant.

∆rH for a reaction is defined as the difference between ∆fH value of products and ∆fH value of reactants.

∆H is negative for exothermic reactions which evolve heat during the reaction and∆H is positive for endothermic reactions which absorb heat from the surroundings.

By the phrase ‘open-handed’ the poet implies to the map of the world that is drawn and reshaped at will by dictators like Hitler who want to gain supreme power over the world.

Sec A = 15/7 Cos A = 1/SecA Therefore CosA = 1/ 15/7 = 7/15 
A + B = 90 or A = 90 - B 

CosA = Cos(90-B) 
7/15 = SinB 
CosecB = 1/SinB = 1/ 7/15 = 15/7 

To select a range of cells, click and hold the left mouse button and drag through the range you want to select. When a range is selected, it becomes highlighted. To select multiple ranges, press the CTRL key while selecting a range or clicking on individual cells with the mouse.

An acid is any hydrogen-containing substance that is capable of donating a proton (hydrogen ion) to another substance. A base is a molecule or ion able to accept a hydrogen ion from an acid.

Acidic substances are usually identified by their sour taste. An acid is basically a molecule which can donate an H+ ion and can remain energetically favourable after a loss of H+. Acids are known to turn blue litmus red.

Properties of Acids

• Acids are corrosive in nature.
• They are good conductors of electricity.
• Their pH values are always less than 7.
• When reacted with metals, these substances produce hydrogen gas.
• Acids are sour-tasting substances.
• Examples: Sulfuric acid [H₂SO₄], Hydrochloric acid [HCl], Acetic acid [CH₃COOH].

Motion of a car on a banked road

In the vertical direction (Y axis)

Ncosϴ = fsinϴ + mg --------------------(i)

In horizontal direction (X axis)

fcosϴ + Nsinϴ = mv²/r  ----------------(ii)

Since we know that f      μ_sN   

For maximum velocity, f = μ_sN

(i)becomes:

       Ncosϴ = μ_sNsinϴ + mg

Or, Ncosϴ - μ_sNsinϴ = mg

Or, N = mg/(cosϴ- μ_ssinϴ)

Put the above value of N in (ii)

μ_sNcosϴ + Nsinϴ = mv²/r 

μ_smgcosϴ/(cosϴ- μ_ssinϴ) + mgsinϴ/(cosϴ- μ_ssinϴ) = mv²/r 

mg (sinϴ + μ_scosϴ)/ (cosϴ - μ_ssinϴ) = mv²/r 

Divide the Numerator & Denominator by cosϴ, we get

v² = Rg (tanϴ +μ_s) /(1- μ_s tanϴ)

v = √ Rg (tanϴ +μ_s) /(1- μ_s tanϴ)

This is the miximum speed of a car on a banked road.

Special case:

When the velocity of the car = v₀ ,

• No f is needed to provide the centripetal force. (μ_s =0)
• Little wear & tear of tyres take place.

             v_o = √ Rg (tanϴ)

 Problem: A circular racetrack of radius 300 m is banked at an angle of 15°. If the coefficient of friction between the wheels of a race-car and the road is 0.2, what is the

 (a) optimum speed of the racecar to avoid wear and tear on its tyres, and

(b) maximum permissible speed to avoid slipping ?

 Solution.

R = 300m

ϴ = 15^o

μ_s  = 0.2

• v_o = √ Rg tanϴ

      = √300 * 9.8 * tan 15^o

      = 28.1 m/s

• v_max = √ Rg (tanϴ +μ_s) /(1- μ_s tanϴ)

             = √ 300 * 9.8 * (0.2 + tan 15^o)/(1-0.2tan15^o)

             = 38.1 m/s

Raja had  ₹ 7.45 .

He bought toffees for ₹ 5.20.

The balance amount left with Raja = 7.45 - 5.20 = ₹ 2.25

Newton’s second law of motion states that the force exerted by a body is directly proportional to the rate of change of its momentum. For a body of mass ‘m’, whose velocity changes from u to v in time t, when force ‘F’ is applied.

Human respiratory system: The human respiratory system begins from nose cavities called nostrils. The air from cavity enters into the pharynx and then into the trachea (or wind pipe). The trachea runs down the neck and divides into two tubes called bronchi. Each bronchi is connected to a lung. In the lungs each bronchi divides into a large number of thin tubes called bronchioles. The bronchioles have a tiny air sac at their ends called alveoli. It is in the alveoli where exchange of gases takes place.
Mechanism of breathing:

1. When we breathe in air, the diaphragm contracts which results in the increase in volume of chest cavity. Due to this expansion of chest cavity, the air pressure in the lungs decreases. Thus, air from outside rushes into the lungs through nostrils, trachea and bronchi. Therefore, air sacs of lungs get filled with air when we breathe in. The exchange of gases between alveoli and blood takes place by the process of diffusion.
   Now, the air present in air sacs of the lungs is rich in C02. When we breathe out air, the diaphragm relaxes which results in the decrease in volume of chest cavity. This contraction pushes the air from the lungs into the trachea, nostrils and then out of the body into air. Breathing in air is called inhalation and breathing out air is called exhalation.
2. Mechanism of gaseous exchange during respiration: The oxygen is carried by blood to all the parts of the body. As the blood passes through the tissues of the body, the oxygen from the blood diffuses into the cell, whereas the C02 which is produced during respiration diffuses into the blood and is carried to the lungs.