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Data : n₁ = 2n₃₂ , (n₁ is octave of n₃₂) beat frequency = 8 Hz 

The set of tuning forks is arranged in descending order of their frequencies.

∴ n₂ = n₁ – 8 

n₃ = n₂ – 8 = n₁ – 2 × 8 

n₄ = n₃ – 8 = n₁ – 3 × 8 

∴ n₃₂ = n₁ – 31 × 8 = n₁ – 248 

Since n₁ = 2n₃₁ , n₃₂ = 2n₃₂ – 248

∴ The frequency of the last fork, n₃₂ = 248 Hz 

The frequency of the first fork, n₁ = 2n₃₂= 2 × 248 = 496 Hz 

∴ The frequency of the 21st fork, n₂₁ = n₁ – 20 × 8 = 496 -160 = 336 Hz

Correct option is (D) 1 : 2.

Linear density of the wire 

= πr²p 

= π(5 × 10^-3)² (8) 

= 2π × 10^-4 g/cm.

The linear density of a string, m = πr²p, where r is the radius of cross section of the string and p is the mass density of its material. By the law of mass of a vibrating string, the frequency of vibrations n of the string is inversely proportional to √m. Therefore, n ∝ 1/r and n ∝ \(\frac 1{\sqrt\mu}\). Hence, the strings of different thicknesses and materials in a stringed musical instrument like sitar can be set to different scales

A progressive wave or wave motion is a periodic or oscillatory disturbance in a medium or in a vacuum that is propagated without any damping and obstruction from one place to another at a finite speed. 

[Note: A progressive wave is also called a traveling wave.]

Correct option is (A) 1/2v 

(1) A pulse travelling on a heavy string will reflect without inversion at its boundary with a lighter string. Thus, a crest will reflect as a crest and a trough will reflect as a trough.

(2) When a pulse travelling on a light string encounters a boundary with a heavier string, the reflected pulse is inverted. Thus, a crest will reflect as a trough and vice versa.

1. A progressive wave in which the vibration of the individual particles of the medium is perpendicular to the direction of propagation of the wave is called a transverse progressive wave. 

2. A progressive wave in which the vibration of the individual particles of the medium is along the line of propagation of the wave is called a longitudinal progressive wave.

(A) a compression reflects as a compression

When a wave travelling in a medium is incident on a boundary with another medium, a part of it returns into the original medium with a change in its direction of propagation while a part of it is transmitted into the second medium. The phenomenon in which a part of the wave is returned into the original medium with reduction in its intensity and energy is called reflection.

Data : m = 3.6 × 10^-3 kg/m, g = 9.8 m/s²

∴ T = 1.8 kg wt = 1.8 × 9.8N

The speed of transverse waves along the string is

v = \(\sqrt{\frac Tm}\) = \(\sqrt{\frac {1.8\times9.8}{3.6\times10^{-3}}}\) = 70 m/s

Data : L = 0.7 m, n (second overtone) = 300 Hz 

In this case, three loops are formed on the string.

∴ L = 3\(\frac λ2\)

∴ λ = \(\frac {2L}3\)

∴ v = nλ = \(\frac {2}3\) nL

∴ v = \(\frac {2}3\) × 300 × 0.7 = 140 m/s

This gives the speed of the wave.

Data : n₁ = 320 Hz, n₂ = 480 Hz Fundamental frequency is n = \(\frac1{2L}\)\(\sqrt{\frac Tm}\)

As the length (L) of the wire and its mass per unit length (m) are kept constant,

n ∝ √T

∴ \(\frac{n_1}{n_2}\) = \(\sqrt{\frac{T_1}{T_2}}\)

∴ The ratio of the tensions in the wire,

\({\frac{T_1}{T_2}}\) = \(({\frac{n_1}{n_2}})^2\) = \(({\frac{320}{480}})^2\) = \(({\frac{2}{3}})^2\) = \(\frac49\)

It would have been successful if it had been well organised and well planned or if it had involved the masses. It would have been successful if merchants, educated middle class and zamindars had supported it and the Indian soldiers had better weapons and goods generals.

Data : L = 0.9 m, n (second overtone) = 324 Hz 

For the second overtone of a vibrating string,

λ = \(\frac23L\)

The speed of the transverse wave formed on the string, v = nλ

∴ v = n × \(\frac23L\) = 324 × \(\frac23\) x 0.9

= 324 × 0.6 = 194.4 m/s

Fundamental frequency, n = \(\frac v{(2L)}\) = \(\frac {50}{(2\times0.25)}\)

= 100 Hz

It was an immediate cause which supplied the spark to ignite diy firewood awaiting to be ignited. Other causes like oppressive economic policy, aggressive annexation policy, religious social interference by the British were already there waiting to be triggered into Revolt. This was provided by the rumour that cartridges were greased with the fat of cow and pig and hence this enraged the Hindus and Muslims.

Mangal Pandey was a sepoy at Barrackpore, who refused to use the greased cartidges in 1857.

Data: l₁ = 16 cm, l₂ = 50.25 cm 

End correction,

e = \(\frac{I_2-3I_1}2\)

= \(\frac{50.25-3\times16}2\) = \(\frac{2.25}2\) = 1.125 cm

Correct option is (D) 1.2 r.

v = 350 m/s, L = 25 cm = 0.25 m

∴ The fundamental frequency of the air column is

n = \(\frac v{4L}\) = \(\frac{350}{4 \times 0.25}\) = 350 Hz

Data : v = 350 m/s, L = 35 cm = 35 × 10^-2 m 

(i) For a pipe closed at one end, the fundamental frequency is

n_c = \(\frac v{4L}\) = \(\frac{350}{4\times35\times10^{-2}}\) = 250 Hz

As only odd harmonics are present in this case, the frequency of pth overtone is n_p = (p × 2 + 1) n_c

∴ The frequency of the 3rd overtone is

n₃ = (3 × 2 + 1)n_c = 7n_c = 7 × 250 = 1750 Hz

(ii) For a pipe open at both ends, the fundamental frequency is

n_O = \(\frac v{2L}\) = \(\frac{350}{2\times35\times10^{-2}}\) = 500 Hz

In this case, all harmonics are present. 

∴ The frequency of the pth overtone is

n_p = (p + 1) n_o

∴ The frequency of the 3rd overtone is n₃ = (3 + 1) n_o = 4n_o = 4 × 500 = 2000 Hz

Data : L = 47 cm = 0.47 m, v = 330 m/s. 

The fundamental frequency of the air column,

n = \(\frac v{2L}\) = \(\frac{330}{2\times0.47}\) = \(\frac{165}{0.47}\) = 351.1 Hz

Data : l = 47 cm = 0.47 m, d = 5 cm = 0.05 m, 

v = 348 m/s 

e = 0.3 d = 0.3 × 0.05 = 0.015 m 

As the tube is open at both ends, the corrected length (L) is 

L = l + 2e = 0.47 + (2 × 0.015) = 0.5 m 

∴ The fundamental frequency of the air column is

n = \(\frac v{4L}\) = \(\frac{348}{2\times0.5}\) = 348 Hz

Sublimation is the process of conversion of a substance from solid state to gaseous state without entering the liquid state. When more pressure is applied, the gaseous particles would come closer and closer (because of compression) and tend to form liquids. The heat energy supplied under pressure will then force the solid to convert into liquid state, as now it cannot sublime due to the pressure applied over it.

Mixture is not formed by the physical mixture of two substances is called.

We are able to walk due to force of friction. Friction is a contact force and arises when two objects are in direct contact with each other. While walking our feet exerts force on the ground pushing it backwards and the ground exerts equal and opposite reaction to our feet helping us to move forward. When we step on banana peel, the friction force between the feet and the peel decreases and we are not able to move forward and slip.

The word ‘fairy tale’ means on account of strange incidents and stories about fairies here.

If we go to the objects of nature affectionately and with friendship, we can make them friends.

If we go to the objects of nature affectionately and with friendship, we can make them friends.

Pandit Nehru found the children in America, Canada and England very like the children of India. So he made friends and played with them a little. The word ‘that’ refers to the playing with the children of those countries.

Pandit Nehru found the children in America, Canada and England very like the children of India. So he made friends and played with them a little. The word ‘that’ refers to the playing with the children of those countries.

The grown ups imagine about themselves that they are different from the people of other countries. Its result is that they deliberately make themselves different from others.

The grown ups imagine about themselves that they are different from the people of other countries. Its result is that they deliberately make themselves different from others.

The resources that : 

1. have not been used traditionally. 

2. are inexhaustible and continuous. 

3. That can be used in various forms again and again are called non-conventional energy resources. 

4. e.g.: solar energy, wind energy, tidal energy, hydal power.

1. Heat energy from the sun is used in solar cookers, solar water heaters, solar driers. 

2. Light energy from the sun is used in solar cells, solar panels.

3. Solar electric plants have the capacity to produce electricity on large scale.

We have great linguistic and religious diversity in our country and in order to preserve this diversity in a sound and healthy manner we have adopted the principle of secularism.

(i) Cooperation

(ii) conflidsw

• There are many languages, religions, cultures, customs and traditions in the Indian society but despite our differences we are living together for many years. 
• This has developed a feeling of oneness amongst us and this oneness has lead to unity in the Indian society.

• I will explain to the children that quarelling with one another is bad. 
• I will advise them to resolve conflicts through understanding and with a spirit of friendship. 
• I will explain to them the importance of tolerance.

I would perform the following functions as the chief minister of the school cabinet:

• Maintain discipline and order in school. 
• Ensure that the different committee members of the school cabinet are doing their duties well. 
• Coordinate with all the ministers to ensure that the day-to-day activities of the school are carried out in an organised manner.

Each individual has several roles and responsibilities and duties of every role are well-defined. While playing these roles, we form bonds with many people. However, changes may occur in the part we play.

• Cooperation makes interdependence in society healthier and allows inclusion of everybody in the society. 
• It is a process of inclusion and of moving ahead, taking along all the sections of society

Conflicts can end when people make effort to understand each other and show a spirit of tolerance.

Laws, traditions.

• I will ensure that I respect all the people of the country. 
• I will develop a secular attitude and work towards national integration.

The tolerance.

Language, religion.