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Posted by Devyanshi Singh 3 years, 1 month ago (13423801)
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Goldi Kumari 3 years, 1 month ago (12972523)
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Posted by Ashmit Kumar 3 years, 1 month ago (13613533)
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Preeti Dabral 3 years, 1 month ago (2983787)
{tex}\begin{aligned} &\frac{3 x}{4-2 x}-\frac{2 x+5}{3}=\frac{5}{2} \\ &\frac{3 x}{4-2 x}=\frac{5}{2}-\frac{5}{3} \\ &\frac{3 x}{4-2 x}=\frac{5}{6} \\ &18 x=5(4-2 x) \\ &18 x=20-10 x \\ &18 x+10 x=20 \\ &38 x=20 \\ &x=\frac{20}{38} \\ &x=\frac{10}{16} \\ &x=\frac{5}{8} \end{aligned}{/tex}
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Preeti Dabral 3 years, 1 month ago (2983787)
As the depth increased the mass of the earth decreases. At the surface of earth this value will be maximum because radius will be maximum. When radius becomes less this value also decreases. Hence acceleration due to gravity decreases with increase in the depth.
Posted by K_Hushii 🍁 3 years, 1 month ago (11720131)
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Preeti Dabral 3 years, 1 month ago (2983787)
A solid cylinder rolling up an inclination is shown in the following figure.

Initial velocity of the solid cylinder, v = 5 m/s
Angle of inclination, {tex}\theta = 30 ^ { \circ }{/tex}
Height reached by the cylinder = h
- Energy of the cylinder at point A will be purely kinetic due to the rotation and translational motion. Hence, total energy at A
= KErot + KEtrans
= {tex}\frac { 1 } { 2 } I \omega ^ { 2 } + \frac { 1 } { 2 } m v ^ { 2 }{/tex}The energy of the cylinder at point B will be purely in the form of gravitational potential energy = mgh
Using the law of conservation of energy, we can write:
{tex}\frac { 1 } { 2 } I \omega ^ { 2 } +\frac { 1 } { 2 } m v ^ { 2 } = m g h{/tex}
Moment of inertia of the solid cylinder, {tex}I = \frac { 1 } { 2 } m r ^ { 2 }{/tex}
{tex}\therefore \frac { 1 } { 2 } \left( \frac { 1 } { 2 } m r ^ { 2 } \right) \omega ^ { 2 } + \frac { 1 } { 2 } m v ^ { 2 } = m g h{/tex}
{tex}\frac { 1 } { 4 } I \omega ^ { 2 } + \frac { 1 } { 2 } m v ^ { 2 } = m g h{/tex}
But we have the relation, {tex}v = r \omega{/tex}
{tex}\therefore \frac { 1 } { 4 } v ^ { 2 } + \frac { 1 } { 2 } v ^ { 2 } = g h{/tex}
{tex}\frac { 3 } { 4 } v ^ { 2 } = g h{/tex}
{tex}\therefore h = \frac { 3 } { 4 } \frac { v ^ { 2 } } { g }{/tex}
{tex}= \frac { 3 } { 4 } \times \frac { 5 \times 5 } { 9.8 } = 1.91 \mathrm { m }{/tex}To find the distance covered along the inclined plane
In {tex}\Delta A B C{/tex}:
{tex}\sin \theta = \frac { B C } { A B }{/tex}
{tex}\sin 30 ^ { \circ } = \frac { h } { A B }{/tex}
{tex}A B = \frac { 1.91 } { 0.5 } = 3.82 \mathrm { m }{/tex}
Hence, the cylinder will travel 3.82 m up the inclined plane. -
{tex}v = \left( \frac { 2 g h } { 1 + \frac { K ^ { 2 } } { R ^ { 2 } } } \right) ^ { \frac { 1 } { 2 } }{/tex}
{tex}\therefore v = \left( \frac { 2 g A B \sin \theta } { 1 + \frac { K ^ { 2 } } { R ^ { 2 } } } \right) ^ { \frac { 1 } { 2 } }{/tex}
For the solid cylinder, {tex}K ^ { 2 } = \frac { R ^ { 2 } } { 2 }{/tex}
{tex}\therefore v = \left( \frac { 2 g A B \sin \theta } { 1 + \frac { 1 } { 2 } } \right) ^ { \frac { 1 } { 2 } }{/tex}
{tex}= \left( \frac { 4 } { 3 } g A B \sin \theta \right) ^ { \frac { 1 } { 2 } }{/tex}
The time taken to return to the bottom is:
{tex}t = \frac { A B } { v }{/tex}
{tex}= \frac { A B } { \left( \frac { 4 } { 3 } g A B \sin \theta \right) ^ { \frac { 1 } { 2 } } } = \left( \frac { 3 A B } { 4 g \sin \theta } \right) ^ { \frac { 1 } { 2 } }{/tex}
{tex}= \left( \frac { 11.46 } { 19.6 } \right) ^ { \frac { 1 } { 2 } } = 0.7645{/tex}
So the total time taken by the cylinder to return to the bottom is (2 {tex}\times{/tex} 0.764)= 1.53 s.as time of ascend is equal to time of descend for the following problem.
Posted by Account Deleted 3 years, 1 month ago (13607212)
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Omya Aryan 3 years, 1 month ago (10989590)
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Posted by Luxmi Bhardwaj 3 years, 1 month ago (13604091)
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Posted by Aryan Kesarwani 3 years, 1 month ago (12527353)
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Preeti Dabral 3 years, 1 month ago (2983787)
sharpening,bluring,Lens correction,lens. blur,noise reduction and liquify vanishing filters.
Posted by Vaibhav Tiwari 3 years, 1 month ago (10448068)
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Posted by Suman Devi 3 years, 1 month ago (13627808)
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Preeti Dabral 3 years, 1 month ago (2983787)
The tiny pores present on the lower surface of leaves is called stomata through which leaves absorb carbon dioxide from air.
Dashdash Kids Student 3 years ago (13730146)
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Posted by Anku Mandal 3 years, 1 month ago (12951806)
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Posted by Anku Mandal 3 years, 1 month ago (12951806)
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Preeti Dabral 3 years, 1 month ago (2983787)
- In olden times, the best way to present an idea was through symbolic personifications. This was the most common and appealing way to invite people's attention.
- From 1789, females appeared in paintings as a symbol of liberty and revolution. Artists, in the eighteenth and nineteenth centuries, often made efforts to represent a country as if it were a person. The female figures were chosen to express an abstract idea of a nation. These female figures, thus, became an allegory of the nation.
- During the French Revolution, many symbolic personifications of 'Liberty' and 'Reason' appeared. In France, the female figure was christened Marianne, which was characterized by Liberty and the Republic - the red cap. the tricolour, the cockade. Statues of Marianne stood in public squares to remind the people of the national symbol of unity.
- Statues of Marianne were erected in public places to remind the public of the national symbol of unity and to persuade them to identify with it.
- Marianne images were marked on coins and stamps,
- Similarly, Germania became the symbol of the German nation. This work was done by the artist Philip Veit. He depicted Germania as a female figure standing against a background where beams of sunlight shone through the tricolour fabric of the national flag. In visual representations, Germania wore the crown of oak leaves, as the German oak stood for heroism. Germania became the allegory of the German nation.
- During the French Revolution, artists used the formal allegory to portray ideas such as Liberty, Justice and the Republic.
Posted by Anku Mandal 3 years, 1 month ago (12951806)
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Preeti Dabral 3 years, 1 month ago (2983787)
Nationalism developed through culture in Europe:
- Culture played an important role in creating the idea of the nation. Art, music, literature and drama helped to express, shape and strengthen nationalist sentiments.
- The cultural movement of Romanticism aimed at developing a particular form of nationalist sentiment. Romantic artists and poets generally focussed on emotions, intuition and mystical feelings and criticized the glorification of reason and science.
- Romantics like the German philosopher Johann Gottfried Herder held the view that true German culture could be discovered only among the common people, the Das Volk. The true spirit of a nation was popularised through folk songs, folk poetry and folk dances.
- The emphasis on vernacular language and the collection of local folklore were used to carry the modern nationalist message to large audiences who were mostly illiterates.
Posted by Anku Mandal 3 years, 1 month ago (12951806)
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Preeti Dabral 3 years, 1 month ago (2983787)
Economic conditions that were viewed as obstacles in nineteenth-century Europe are as follows:
- The absence of freedom of markets. State-imposed restrictions on the movement of goods and capital.
- Napoleon's administration had created a different currency. weights, and measure for each of the 39 states in the confederation. Conversion of weights and measures for each region created time-consuming calculations and complications.
- There were 11 custom barriers and 5% customs duty at each for carrying goods from one place to another.
- The first half of the 19th century had low explosive population growth. Job-seekers were more and employment opportunities were less.
- Small producers faced stiff competition from the import of cheap machine-made goods. Peasants struggled under the burden of feudal dues.
Posted by Anku Mandal 3 years, 1 month ago (12951806)
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Preeti Dabral 3 years, 1 month ago (2983787)
- At the very beginning, the artisans, businessmen and peasants enjoyed the newly-found freedom.
- They welcomed the standardised weights and measures, uniform laws and a common currency for the entire nation as they realised that these would be more helpful in trade and in facilitating the movement and exchange of goods and capital from one area to another.
- An outweighing of the advantages of administrative changes were witnessed in the Increase in taxes, censorship and forced conscription in French armies.

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Saini.Satwinder Saini Satwinder 3 years, 1 month ago (13334050)
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