Find the rate of change of the total surface area of a cylinder of radius r and height h, when the radius varies.
Question: Find the rate of change of the total surface area of a cylinder of radiusrand heighth, when the radius varies. Solution: LetTbe the total surface area of a cylinder. Then, $T=2 \pi r(r+h)$ Since the radius varies, we differentiate the total surface area w.r.t. radiusr. Now, $\frac{d T}{d r}=\frac{d}{d r}[2 \pi r(r+h)]$ $\Rightarrow \frac{d T}{d r}=\frac{d}{d r}\left(2 \pi r^{2}\right)+\frac{d}{d r}(2 \pi r h)$ $\Rightarrow \frac{d T}{d r}=4 \pi r+2 \pi h$ $\Rightarrow \frac{d T}{d r}=2...
Read More →Manu was heating oil to fry potato chips.
Question: Manu was heating oil to fry potato chips. The cooking oil all of a sudden caught fire, he poured water to extinguish the fire. Do you think, this action was suitable? If yes, why? If not, why not? In such a condition what should Manu have done? Solution: Pouring water to extinguish the fire due to oil was not suitable action. It is because oil is lighter than water. So, water will settle down below the oil. The oil floats on water and continues to burn. In such condition, sand or soil ...
Read More →A ladder, 5 metre long, standing on a horizontal floor,
Question: A ladder, 5 metre long, standing on a horizontal floor, leans against a vertical wall. If the top of the ladder slides down wards at the rate of 10 cm/sec, then find the rate at which the angle between the floor and ladder is decreasing when lower end of ladder is 2 metres from the wall. Solution: Length of the ladder $=500 \mathrm{~cm}$ Let the horizontal length covered between the wall and the ladder be $x$ and vertical length covered between the wall and the ladder be $y$ And let th...
Read More →You are provided with three
Question: You are provided with three watch glasses containing milk, petrol and mustard oil respectively. Suppose you bring a burning candle near these materials one by one, which material(s) will catch fire instantly and why? Solution: The watch glass containing petrol will catch fire instantly because its ignition temperature is very low. Also, petrol is an inflammable substance, i.e. it can easily catch fire with a flame....
Read More →Cracker on ignition produces
Question: Cracker on ignition produces sound. Why? Solution: When a cracker is ignited, a sudden reaction (very rapid) takes place with the evolution of heat, light and sound and a large amount of gas is liberated. Such a reaction is called explosion. The gases produced are heated by the heat evolved in the reaction. The hot gases expand rapidly and cause an explosion (producing a loud sound)....
Read More →Write True/False against the following statements
Question: Write True/False against the following statements and also correct the false statement. (a) A physical process in which a substance reacts with oxygen to give off heat is called combustion. (b) Water is the best extinguisher for fires involving electrical equipment. (c) Alcohol, CNG and LPG are inflammable substances. (d) Increased concentration of nitrogen in air is believed to cause global warming. (e) Greater the calorific value, better is the fuel. (f) Middle zone is the hottest zo...
Read More →The amount of pollution content added in air in a city due to x diesel vehicles is given by
Question: The amount of pollution content added in air in a city due to $x$ diesel vehicles is given by $P(x)=0.005 x^{3}+0.02 x^{2}+30 x$. Find the marginal increase in pollution content when 3 diesel vehicles are added and write which value is indicated in the above questions. Solution: Since, marginal increase in the pollution content is the rate of change of total pollution with respect to the number of diesel vehicles, we have Marginal increase in pollution $=\frac{\mathrm{d} P}{\mathrm{~d}...
Read More →People usually keep angithi/burning
Question: People usually keep angithi/burning coal in their closed rooms during winter season. Why is it advised to keep the door open? Solution: When coal burns in air, it produces carboh dioxide which is non-poisonous. But, when angithi or coal burns in a closed room, the air or oxygen cannot enter the room. So, in the incomplete supply of oxygen, coal burns to produce carbon monoxide which is highly poisonous gas. It causes suffocation in a closed room. So, door and windows should be open....
Read More →Fill in the blanks using the words given in the box.
Question: Fill in the blanks using the words given in the box. ignition, petrol, combustion, calorific value, combustible, inflammable (a) A chemical process in which a substance reacts with oxygen to give off heat is called (b) Wood, paper, CNG are substances. (c) The lowest temperature at which a substance catches fire is called its temperature. (d) Ignition temperature of is lower than that of wood. (e) The substances which have very low temperature and can easily catch fire with a flame are ...
Read More →If you hold a piece of iron wire with a pair of tongs
Question: If you hold a piece of iron wire with a pair of tongs inside a candle flame or a Bunsen burner flame, what will you observe? Will it produce a flame? Solution: Iron wire will become red hot and glow. It will not produce a flame....
Read More →Find the sum of the series:
Question: Find the sum of the series: $(1 \times 2)+(2 \times 3)+(3 \times 4)+(4 \times 5)+\ldots$ to $n$ terms Solution: In the given question we need to find the sum of the series. For that, first, we need to find the nth term of the series so that we can use summation of the series with standard identities and get the required sum. The series given is $(1 \times 2)+(2 \times 3)+(3 \times 4)+(4 \times 5)+\ldots$ to $n$ terms. The series can be written as, $[(1 \times(1+1)),(2 \times(2+1))$, $(...
Read More →State whether the following statements are True/False.
Question: State whether the following statements are True/False. (i) Air is necessary for combustion. (ii) Magnesium is a non-combustible metal. (iii) Carbon dioxide is an excellent fire extinguisher. (iv) Calorific value of wood is higher than that of coal. Solution: 1. True, air contains oxygen and oxygen is a supporter of combustion. 2. False, magnesium is a combustible metal. 3.True 4.False, calorific value of coal is higher than that of wood....
Read More →Boojho wants to separate the following materials
Question: Boojho wants to separate the following materials as combustible and non-combustible. Can you help him? Charcoal, chalk, stone, iron rod, copper coin, straw, cardboard, glass, paper, candle, wood. Solution: 1.Combustible charcoal, straw, cardboard, paper, candle, wood. 2.Non-combustible chalk, stone, iron rod, copper coin, glass....
Read More →Why is the use of diesel and petrol
Question: Why is the use of diesel and petrol as fuels in automobiles being replaced by Compressed Natural Gas (CNG) in big cities? Solution: It is because when CNG burns, it produces harmful products in very small amount. It is a clean fuel because it burns without producing smoke. The use of CNG as fuel in automobiles has reduced air pollution In big cities....
Read More →Anu wants to boil water quickly in a test tube.
Question: Anu wants to boil water quickly in a test tube. On observing the j different zones of the flame, she is not able to decide which zone of the flame will be best for boiling water quickly. Help her in this activity. Solution: Anu should keep her test tube in the outermost zone or non-luminous zone of the flame because it is the hottest zone of a flame and has more temperature. In the outer zone of a flame, complete combustion of the fuel takes place because there is plenty of air around ...
Read More →Two glass jars A and B ajre filled with carbon dioxide
Question: Two glass jars A and B ajre filled with carbon dioxide and oxygen gases respectively. In each jar, a lighted candle is placed simultaneously. In which jar, will the candle remain lighted for a longer time and why? Solution: In jar B, the candle remains lighted for a longer time because oxygen is a supporter of combustion. So, we can say that oxygen (air) is necessary for combustion to take place....
Read More →If the rate of change of volume of a sphere is equal to the rate of change of its radius, find the radius of the sphere.
Question: If the rate of change of volume of a sphere is equal to the rate of change of its radius, find the radius of the sphere. Solution: LetrbetheradiusandVbethevolumeofthesphereatanytimet. Then, $V=\frac{4}{3} \pi r^{3}$ $\Rightarrow \frac{d V}{d t}=4 \pi r^{2} \frac{d r}{d t}$ $\Rightarrow 4 \pi r^{2}=1 \quad\left[\because \frac{d V}{d t}=\frac{d r}{d t}\right]$ $\Rightarrow r^{2}=\frac{1}{4 \pi}$ $\Rightarrow r=\sqrt{\frac{1}{4 \pi}}$ $\Rightarrow r=\frac{1}{2 \sqrt{\pi}}$ units...
Read More →If the rate of change of volume of a sphere is equal to the rate of change of its radius, find the radius of the sphere.
Question: If the rate of change of volume of a sphere is equal to the rate of change of its radius, find the radius of the sphere. Solution: LetrbetheradiusandVbethevolumeofthesphereatanytimet. Then, $V=\frac{4}{3} \pi r^{3}$ $\Rightarrow \frac{d V}{d t}=4 \pi r^{2} \frac{d r}{d t}$ $\Rightarrow 4 \pi r^{2}=1 \quad\left[\because \frac{d V}{d t}=\frac{d r}{d t}\right]$ $\Rightarrow r^{2}=\frac{1}{4 \pi}$ $\Rightarrow r=\sqrt{\frac{1}{4 \pi}}$ $\Rightarrow r=\frac{1}{2 \sqrt{\pi}}$ units...
Read More →Some words (underlined) in the
Question: Some words (underlined) in the following sentences are jumbled up. Write them in theirjrorrect form. (a) Seldie is a combustible substance. (b) Slaas is a non-combustible material. (c) Chittsmack does not burn by itself. (d) Some substances on combustion produce thea and mafel. (e) The amount of heat energy produced on complete combustion of 1 kg of a fuel is called its ficalroic value. Solution: (a) Diesel (b) Glass (c) Matchstick (d) heat, flame (e) calorific...
Read More →Find the surface area of a sphere when its volume is changing at the same rate as its radius.
Question: Find the surface area of a sphere when its volume is changing at the same rate as its radius. Solution: Let $r$ be the radius and $V$ be the volume of the sphere at any time $t .$ Then, $V=\frac{4}{3} \pi r^{3}$ $\Rightarrow \frac{d V}{d t}=4 \pi r^{2}\left(\frac{d r}{d t}\right)$ $\Rightarrow \frac{d V}{d t}=4 \pi r^{2}\left(\frac{d V}{d t}\right) \quad\left[\because \frac{d V}{d t}=\frac{d r}{d t}\right]$ $\Rightarrow 4 \pi r^{2}=1$ $\Rightarrow$ Surface area of sphere $=1$ square un...
Read More →Fill in the blanks.
Question: Fill in the blanks. (a)A .. process in which a substance reacts with .. to give off heat is called combustion. (b) When the clothes of a person catch the person is covered with a to extinguish fire. (c) The.. temperature at which a substance catches fire is called its..temperature. (d) The substances which gave very ..ignition temperature and can easily catch fire with a flame are called.substances. (e) The substances which vaporise during..give flame. Solution: (a) chemical, oxygen (b...
Read More →Shyam was cooking potato curry on a chulha.
Question: Shyam was cooking potato curry on a chulha. To his surprise, he observed that the copper vessel was getting blackened from outside. It may be due to (a) proper combustion of fuel (b) improper cooking of potato curry (c) improper combustion of fuel (d) burning of copper vessel Solution: (c) Due to incomplete combustion of fuel, copper vessel was getting blackened from outside....
Read More →Find the sum of the series:
Question: Find the sum of the series: $\left(5^{2}+6^{2}+7^{2}+\ldots+20^{2}\right)$ Solution: In the given question we need to find the sum of the series. For that, first, we need to find the nth term of the series so that we can use summation of the series with standard identities and get the required sum. The series given is $5^{2}, 6^{2}, 7^{2} \ldots 20^{2}$. The series can be written as, $\left[(1+4)^{2},(2+4)^{2},(3+4)^{2} \ldots(16+4)^{2}\right]$ So, $\mathrm{n}^{\text {th }}$ term of th...
Read More →The side of an equilateral triangle is increasing at the rate
Question: The side of an equilateral triangle is increasing at the rate of $\frac{1}{3} \mathrm{~cm} / \mathrm{sec}$. Find the rate of increase of its perimeter. Solution: LetxbethesideandPbetheperimeteroftheequilateraltriangleatanytimet.Then, $P=3 x$ $\Rightarrow \frac{d P}{d t}=3 \frac{d x}{d t}$ $\Rightarrow \frac{d P}{d t}=3 \times \frac{1}{3}$ $\left[\because \frac{d x}{d t}=\frac{1}{3} \mathrm{~cm} / \mathrm{sec}\right]$ $\Rightarrow \frac{d P}{d t}=1 \mathrm{~cm} / \mathrm{sec}$...
Read More →The side of an equilateral triangle is increasing at the rate
Question: The side of an equilateral triangle is increasing at the rate of $\frac{1}{3} \mathrm{~cm} / \mathrm{sec}$. Find the rate of increase of its perimeter. Solution: LetxbethesideandPbetheperimeteroftheequilateraltriangleatanytimet.Then, $P=3 x$ $\Rightarrow \frac{d P}{d t}=3 \frac{d x}{d t}$ $\Rightarrow \frac{d P}{d t}=3 \times \frac{1}{3}$ $\left[\because \frac{d x}{d t}=\frac{1}{3} \mathrm{~cm} / \mathrm{sec}\right]$ $\Rightarrow \frac{d P}{d t}=1 \mathrm{~cm} / \mathrm{sec}$...
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