Using a protractor, draw each of the following angles.
Question: Using a protractor, draw each of the following angles. $-400^{\circ}$ Solution: The given angle is negative Adding or subtracting $360^{\circ}$ from a particular angle does'nt changes its position. Therefore, Angle can also be written as $=-400^{\circ}+360^{\circ}=-40^{\circ}$ The angle is still negative, so we will further add $360^{\circ}$ to it. Therefore, Angle can also be written as $=-40^{\circ}+360^{\circ}=320^{\circ}$ - Draw a straight line AB. - Place a dot at B. This dot repr...
Read More →Show that the relative error in computing the volume of a sphere,
Question: Show that the relative error in computing the volume of a sphere, due to an error in measuring the radius, is approximately equal to three times the relative error in the radius. Solution: Letxbe the radius of the sphere andybe its volume. Let $\Delta x$ be the error in the radius and $\Delta V$ be the approximate error in the volume. $y=\frac{4}{3} \pi x^{3}$ $\Rightarrow \frac{d y}{d x}=4 \pi x^{2}$ $\Rightarrow \Delta y=d y=\frac{d y}{d x} d x=4 \pi x^{2} \times \Delta x$ $\Rightarr...
Read More →Using a protractor, draw each of the following angles.
Question: Using a protractor, draw each of the following angles. $-310^{\circ}$ Solution: The given angle is negative Adding or subtracting $360^{\circ}$ from a particular angle does'nt changes its position. Therefore, Angle can also be written as $=-310^{\circ}+360^{\circ}=50^{\circ}$ - Draw a straight line AB. - Place a dot at B. This dot represents the vertex of the angle. - Place the centre of the protractor at B and the baseline of the protractor along the arm BA. - Find $50^{\circ}$ on the...
Read More →While travelling on a rickshaw,
Question: While travelling on a rickshaw, you might have experienced that if the seat cover is very smooth, you tend to slip when brakes are applied suddenly. Explain. Solution: If the seat cover of rickshaw is very smooth, then the friction between our body and the seat is very small. Therefore, when the brakes are applied, we tend to slip....
Read More →Show that the relative error in computing the volume of a sphere,
Question: Show that the relative error in computing the volume of a sphere, due to an error in measuring the radius, is approximately equal to three times the relative error in the radius. Solution: Letxbe the radius of the sphere andybe its volume. Let $\Delta x$ be the error in the radius and $\Delta V$ be the approximate error in the volume. $y=\frac{4}{3} \pi x^{3}$ $\Rightarrow \frac{d y}{d x}=4 \pi x^{2}$ $\Rightarrow \Delta y=d y=\frac{d y}{d x} d x=4 \pi x^{2} \times \Delta x$ $\Rightarr...
Read More →We have two identical metal sheets.
Question: We have two identical metal sheets. One of them is rubbed with sand paper and the other with ordinary paper. The one rubbed with sand paper shines more than the other. Give reason. Solution: While rubbing with sandpaper, more frictional force is produced between the layers of metal sheet and sandpaper which causes more force on dust particles and they are removed easily, so it will shine more. But in case of ordinary paper, the force of friction is not sufficient to remove all the dust...
Read More →When the cutting edge of a knife is put
Question: When the cutting edge of a knife is put against a fast rotating stone to sharpen it, sparks are seen to fly. Explain the reason. Solution: Due to the friction between cutting edge of a knife and stone, the temperature of the knife and hence stone increases and it increases to such a level that the sparks are produced which can be seen while sharpening it....
Read More →A father and son pushed their car to bring
Question: A father and son pushed their car to bring it to the side of road as it had stalled in the middle of the road. They experienced that although they had to push with all their might initially to move the car, the push required to keep the car rolling was smaller, once the car started rolling. Explain. Solution: When the car is at rest, we have to apply greater force to set the car in motion which value is more. As the car starts moving, the friction changes into the rolling friction whic...
Read More →The height of a cone increases by k%,
Question: The height of a cone increases byk%, its semi-vertical angle remaining the same. What is the approximate percentage increase (i) in total surface area, and (ii) in the volume, assuming thatkis small? Solution: Lethbe the height,ybe the surface area,Vbe the volume,lbe the slant height andrbe the radius of the cone. Let $\Delta h$ be the change in the height, $\Delta r$ be the change in the radius of base and $\Delta l$ be the change in the slant height. Semi - vertical angle ramaining t...
Read More →Using a protractor, draw each of the following angles.
Question: Using a protractor, draw each of the following angles. $-220^{\circ}$ Solution: Given angle can be completely written in degree as $=-220^{\circ}$ $-220^{\circ}=360^{\circ}-220^{\circ}=140^{\circ}$...
Read More →The height of a cone increases by k%,
Question: The height of a cone increases byk%, its semi-vertical angle remaining the same. What is the approximate percentage increase (i) in total surface area, and (ii) in the volume, assuming thatkis small? Solution: Lethbe the height,ybe the surface area,Vbe the volume,lbe the slant height andrbe the radius of the cone. Let $\Delta h$ be the change in the height, $\Delta r$ be the change in the radius of base and $\Delta l$ be the change in the slant height. Semi - vertical angle ramaining t...
Read More →A marble is allowed to roll down an inclined
Question: A marble is allowed to roll down an inclined plane from a fixed height. At the foot of the-inclined plane, it moves on a horizontal surface (a) covered with silk cloth (b) covered with a layer of sand and (c) covered with a glass sheet. On which surface, will the marble move the shortest distance. Give reason for your answer. Solution: Marble will move the shortest distance on the layer of sand because it will exert a greater force of friction on the marble and other two surfaces like ...
Read More →Using a protractor, draw each of the following angles.
Question: Using a protractor, draw each of the following angles. $-40^{\circ}$ Solution: The given angle is negative Adding or subtracting $360^{\circ}$ from a particular angle does'nt changes its position. Therefore, Angle can also be written as $=-40^{\circ}+360^{\circ}=320^{\circ}$ - Draw a straight line AB. - Place a dot at B. This dot represents the vertex of the angle. - Place the centre of the protractor at B and the baseline of the protractor along the arm BA. - Find $320^{\circ}$ on the...
Read More →Explain why the surface of mortar
Question: Explain why the surface of mortar and pestle (silbatta) used for grinding is etched again after prolonged use. Solution: After prolonged use, the mortar and pestle loose the roughness, due to which frictional force reduces and it does not work properly. So, we have to etch it to makelt rough again....
Read More →The handle of a cricket bat or a badminton
Question: The handle of a cricket bat or a badminton racquet is usually rough. Explain the reason. Solution: The handle of a cricket bat or a badminton racquet is rough, so that while playing, the bat or badminton racquet does not slip away from the hands of the player. Roughness is responsible for the frictional force between handle of the bat or a badminton racquet andhands, without which gripping is not possible....
Read More →Using a protractor, draw each of the following angles.
Question: Using a protractor, draw each of the following angles. $430^{\circ}$ Solution: The given angle is greater than 360 Adding or subtracting $360^{\circ}$ from a particular angle does'nt changes its position. Therefore, Angle can also be written at as $=430^{\circ}-360^{\circ}=70^{\circ}$ - Draw a straight line AB. - Place a dot at B. This dot represents the vertex of the angle. - Place the centre of the protractor at B and the baseline of the protractor along the arm BA. - Find $70^{\circ...
Read More →Cartilage is present in the joints of our body
Question: Cartilage is present in the joints of our body which helps in their smooth movement. With advancing age, this cartilage wears off. How would this affect the movement of joints? Solution: Cartilage is present in the joints of our body, reduces friction during movement of joints. But on wearing off this cartilage, the force of friction increases due to which the smoothness of movement decreases and one feels the joint pain....
Read More →Is there a force of friction between
Question: Is there a force of friction between the wheels of a moving train and iron rails? If yes, name the type of friction. If an air cushion can be introduced between the wheel and the rail, what effect will it have on the friction? Solution: Yes, there is always a force of friction between the wheels of a moving train and iron rails. The name of this friction is rolling friction, since the wheels are rolling on the track. On introducing air cushion, the frictional force becomes less, since ...
Read More →You might have noticed that when
Question: You might have noticed that when used for a long time, slippers with rubber soles become slippery. Explain the reason. Solution: It is due to continuousrubbing of soles with the ground, the spikes on the sole get damaged slowly and the soles become slippery....
Read More →Imagine that an object is falling through
Question: Imagine that an object is falling through a long straight glass tube held vertical, air has been removed completely from the tube. The object does i not touch the walls of the tube. Will the object experience any force of friction? Solution: No, the object will not experience any frictional force because to experience the force of friction, two surfaces must be there and there is only one surface in this case....
Read More →The pressure p and the volume v
Question: The pressurepand the volumevof a gas are connected by the relationpv1.4= const. Find the percentage error inpcorresponding to a decrease of 1/2% inv. Solution: We have $p v^{1.4}=$ constant $=k$ (say) Taking log on both the sides, we get $\log \left(p v^{1.4}\right)=\log k$ Differentiating both the sides w.r.t. $x$, we get $\frac{1}{p} \frac{d p}{d v}+\frac{1.4}{v}=0$ $\Rightarrow \frac{d p}{p}=\frac{-1.4 d v}{v}$ Now, $d p=\frac{d p}{d v} d v=\frac{-1.4 p}{v} d v$ $\Rightarrow \frac{d...
Read More →Using a protractor, draw each of the following angles.
Question: Using a protractor, draw each of the following angles. $300^{\circ}$ Solution: - Draw a straight line $A B$. - Place a dot at B. This dot represents the vertex of the angle. - Place the centre of the protractor at B and the baseline of the protractor along the arm BA. - Find $300^{\circ}$ on the scale and mark a small dot at the edge of the protractor. - Join the vertex $B$ to the small dot with a ruler to form the second arm, $B C$, of the angle. - Mark the angle with a small arc as s...
Read More →Two boys are riding their bicycles on
Question: Two boys are riding their bicycles on the same concrete road. One has new tyres on his bicycle while the other has tyres that are old and used. Which of them is more likely to slip while moving through a patch of the road which has lubricating oil spilled over it? Solution: The boy having the tyres which are old and used is most likely to slip because these tyres will experience less friction force which is insufficient to move on the oily road....
Read More →Will force of friction come
Question: Will force of friction come into play when a rain drop rolls down a glass window pane? Solution: Yes, friction comes into play when two surfaces are in contact, e.g. glass and water in this case.....
Read More →In a large commercial complex
Question: In a large commercial complex there are four ways to reach the main road. One of the path has loose soil, the second is laid with polished marble, the third is laid with bricks and the fourth has gravel surface. It is raining heavily and Paheli wishes to reach the main road. The path on which she is least likely to slip is (a) loose soil (b) polished marble (c) bricks (d) gravel Solution: (d) She should use gravel surface path because only in this path. She will have sufficient frictio...
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