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Gain in dB = 10 log₁₀ A
50 = 10 log₁₀A_p
5 = log₁₀ A_p
log₁₀ A_p = 5
A_p = 10⁵
∴ log_a N = x ⇒ a^x = N.

(i) Stabilisation of the gain.

(ii) Increase in input impedance.

(iii) Decrease in output impedance.

(iv) Increase in bandwidth.

(v) Reduction in noise and distortion.

BW = (1 + Aβ)BW
= (1 + 100 x 0.1) x 300kHz
= 3,300kHz

Gain in dB = 20 log A_v
= 20 log 10⁵
= 20 x 5 log₁₀10
= 100 x 1 = 100 dB.

A= 200,
β = 0.1,
BW = 20 kHz .
Gain with feedback is BW_F
= (1 + Aβ) BW
= (1 + 200 x 0.1) x 20 kHz
= 21 x 20 kHz
= 420 kHz    

Gain bandwidth of an amplifier is always a constant.

Volume of rainfall = lbh 

= 6 × 4 × 0.01 

= 0.24 m³ 

∵ Volume of water in cylindrical vessel = volume of rainfall 

∴ πr²h = 0.24 

⇒ h = \(\frac{0.24\times7}{22\times0.2^2}\)

⇒ h ≈ 1.91m = 191 cm

The quantity which has maximum power (n) should be measured most accurately because any error in the measurement of this quantity is multiplied n times in the final result.

\(I_1= \frac{2}{5}MR^2,I_2=\frac{2}{5}M(\frac{R}{2})^2\)

or \(I_2=\frac{I_1}{4}\)

\(I_1w_1=I_2w_2\)

\(I(\frac{2π}{T_1})=\frac{1}{4}I(\frac{2π}{T_2})\)

\(T_2= \frac{T_1}{4}=\frac{24}{4}=6\, hours\)

I (first case) > 1 (Second case) 

∴ \(\tau\) r = l α 

⇒ α (first case) < α (second case)

The center of gravity of a body is the point at which the entire weight of the body acts, irrespective of the position and orientation of the body.

• Transnational motion - A book resting on a table.
• Rotational equilibrium - A body moves in a circular path with constant velocity.
• Static equilibrium - A wall - hanging, hanging on the wall.
• Dynamic equilibrium - A ball decends down in a fluid with its terminal velocity
• Stable equilibrium - A table on the floor
• Unstable equilibrium - A pencil standing on its tip.
• Neutral equilibrium - A dice rolling on a game board.

Here, m₁ = 2 kg, m₂ = 3 kg and m₃ = 5 kg

(a) When the system is moving upward with an acceleration 'a' where a = 2 ms^-2.

As per the fig., consider the free body diagram of the system of three blocks. Then,

T₁ - (m₁ + m₂ + m₂) g = (m₁ + m₂ + m₃) a

or, T₁ = (m₁ + m₂ + m₃) (a + g)    ...(i)

or, T₁ = (2 + 3 + 5) x (2 x 9.8) = 118 N

Consider the free body diagram of blocks of masses m₂ and m₃. Then

T₂ - (m₂ + m₃)g = (m₂ + m₃) x a     ....(ii)

or, T₂ = (m₂ + m₃)(a + g)

⇒ T₂ = (3 + 5) x (2 x 9.8) = 94.4 N

Consider the free body diagram of block of mass m₃. Then,

T₃ - m₃g = m₃a    ....(iii)

or, T₃ = m₃(g + a) = 5 x (2 + 9.8) = 59 N

(b) When the system is held stationary:

Obviously, a = 0, setting a = 0, in the equations (i), (ii) and (iii), we have

T₁ = (m₁ + m₂ + m₃) g = (2 + 3 + 5) x 9.8

= 98 N

T₂ = (m₂ + m₃) g = (3 + 5) x 9.8 = 78.4 N

and T₃ = m₃g = 5 x 9.8 = 49 N

Correct answer is (c) \(\sqrt2 \) v₀

Torque is defined as the moment of the external applied force about a point or axis of rotation. The expression for torque is,

\(\vec \tau\)= \(\vec r\) x \(\vec F\)

(a) straight line

(iii) ताप बढ़ने पर बढ़ती है।

(iv) दोनों, अधिक संख्या में इलेक्ट्रॉन तथा अल्प संख्या में कोटर (होल)

इसमें त्रिसंयोजी अपद्रव्य (ऐलुमिनियम) मिलाकर।

चालकता बढ़ जाती है।

चालन बैंड तथा संयोजकता बैंड के बीच ऊर्जा अन्तराल कार्बन के लिए सबसे अधिक, सिलिकॉन के लिए उससे कम तथा जर्मेनियम के लिए सबसे कम होता है; अतः (c) प्रकथन सत्य है।

यहाँ A₁ = 10 तथा A₂ = 20 V_i = 0.01 वोल्ट 

अतः कुल वोल्टता लाभ A = A₁ x A₂ = 10 x 20 = 200 

परन्तु A = vo/v_i ⇒  निर्गत वोल्टता V₀ = A x V_i 

V₀ = (200 x 0.01) वोल्टे = 2 वोल्ट

A cyclotron is a cyclic magnetic resonance accelerator in which an alternating potential difference of a few kV is used to accelerate light positive ions such as protons, deuterons, α-particles, etc., but not electrons, to very high energies of the order of a few MeV. It was developed by E. O. Lawrence and M. S. Livingston in 1932.

Principle: The cyclotron employs the principle of synchronous acceleration to accelerate charged particles which describe a spiral path at right angles to a constant magnetic field and make multiple passes through the same alternating p.d., whose frequency is the same as the frequency of revolution of the particles.

The answer is (A) Photoelectric effect

The answer is (A) zero

यह आवश्यक नहीं है कि निकट दृष्टिदोष अथवा दूर दृष्टिदोष केवल नेत्र के आंशिक रूप से अपनी समंजन क्षमता खो देने के कारण ही उत्पन्न होता है। यह नेत्र गोलक के सामान्य आकार से बड़ा अथवा छोटा होने के कारण भी उत्पन्न हो सकता है।

1. celestial objects : The objects in the sky are called celestial objects. 

2. celestial sphere : The imaginary sphere centered around us is called celestial sphere. 

3. horizon : The imaginary circle along which the sky appears to meet the ground is called the horizon.

1. True

2. False

1. True

2. True

1.False

2.False

(a) Cassiopeia

Correct answer is (a) Mars

(b) solidified carbon dioxide

(a) lowest density

1. A person in England can recognize the pole star easily than a person in Bangalore : Pole star appears to be stationary above the Earth’s North Pole, since England lies in the Northern side Northern hemisphere a person in England can recognize pole star than a person in Bangalore. 

2. Mercury in difficult to observe : It is very difficult to observe mercury because it is very close to the sun and most the time it is hidden by the glare of the sun. However it can be seen just before sunrise and just after sunset. 

3. A day on Venus is longer than its year : The period of rotation of Venus is 243 days and the period of revolution is 224 days. Since period of rotation is longer than period of revolution, a day on Venus is longer than its year. 

4. Green house effect is prominent on Venus : Venus is composed mostly of carbon dioxide. There are several layers of clouds many kilo meters thick composed of sulfuric acid. This dense atmosphere of carbon-dioxide blocks the long wavelength infrared radiation and heat is trapped inside, hence the green house effect is prominent on Venus.

Our solar system comprises of the following: 

1. The sun which is the center of the solar system. 

2. Eight planets are mercury, Venus, Earth, mars, Jupiter, saturnuranus and Neptune, 

3. The Asteroid belt between the orbits of mars and Jupiter 

4. Satellites of the planets, which are also Called the moons of the planets. 

5. Comets such as Halley. 

6. Artificial Satellites and space crafts,

1. light minutes 10 × 60 × 300000 

= 180000000 km 

= 180 million km

2. 10 light days 10 × 24 × 60 × 60 × 300000 

= 259300000000 km 

= 259200 million km

3. 10 light years 10 × 365 × 24 × 60 × 60 × 300000 

= 94608000000000 

= 94608000 million km.

Newton’s first law of motion states that, everybody continues to be in its state of rest or uniform motion along a straight line unless compelled to change its state by an external force. Newton’s second law of motion states that the rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction of the force. Newton’s third law of motion states that for every action there is. an equal and opposite reaction. 

Illustrations for Newton’s third law of motion are

• when a book is placed on the table the book exerts force on the table (action), in turn the table exerts an equal and opposite force (reaction) on the book in the upward direction. 
• The sailing of a boat is due to the action of the boat on water and the reaction from water on boat.

In a satellite of Jupiter has active volcanoes.

Planets: 

1. planets are natural celestial objects 

2. planets revolve round the sun 

3. planets are big in size Satellites: 

4. Satellites may be natural or artificial objects. 

5. Satellites revolve round the planets. 

6. Satellites are smaller in size than planets.

1. Saturn 

2. Venus 

3. Mercury 

4. Jupiter

Venus planet is called morning star or evening star.

Rocket propulsion.

There are two types of friction :

(i) Static friction : This type of friction acts till the body does not move, therefore this type of friction is known as static friction. The maximum static friction is known as “Limiting friction”.

(ii) Dynamic or kinetic friction : When the body starts moving,then the acting friction is known as dynamic or kinetic friction. Its value is some less than the limiting friction.

Static Frictional Force : Static friction is the friction that exists between a stationary object and the surface on which it resting. Static friction keeps an object at rest. It must is overcome to start moving the object.

Imagine trying to push an object across the floor. You push on it with a small force, but it does not move, this is because it is not accelerating. However, according to Newton’s second law, the object must move with an acceleration.
a = \(\frac{F}{m}\)

Now, as the body remains at rest, it implies that an opposing force equal to the applied force must have come into play resulting in zero net force on the object. This force is called static friction. It is denoted by F_s.

Thus, static friction is the opposing force that comes into play when one body tends to move over the surface of another, but the actual motion has not started.

• The static friction depends upon the nature of surfaces of the two bodies in contact.
• The static friction does not exist by itself. When there is no applied force, there is no static friction. It comes into play only when the applied force tends to move the body.
• The static friction is a self-adjusting force.

Limiting Friction : If the applied force is increased, the force of static friction also increases. If the applied force exceeds a certain (maximum) value, the body starts moving. This maximum value of static friction up to which the body does not move, is called limiting friction.

1. The magnitude of limiting: friction between any two bodies in contact is directly proportional to the normal reaction between them.
(f_s)_max ∝ N
(f_s) _max ∝ μ_s N ………….. (1)

Where the constant of proportionality p s is called the coefficient of static friction. Its value depends upon the nature of surfaces of the two bodies in contact that means whether dry or wet; rough or smooth; polished or non polished. For example, when two polished metal surfaces are in contact, ps = 0.2, when these surface are lubricated, μ_s = 0.1
The value of μ_s lies between 0 and 1 or 0 < μ_s < 1
∵ N = Mg
(F_s)_max = μ_s m_g ……………… (2)

2. Direction of the force of limiting friction is always opposite to the direction in which one body is at the verge of moving over the other.

3. Coefficient of Static Friction :
μ_s is called coefficient of static friction and is defined as the ratio of force of limiting friction and normal reaction
From(1), μ_s = \(\frac{\left(f_{s}\right)_{\max }}{N}\)
Dimension: [M⁰L⁰T⁰]
Unit: It has no unit.
Value of μ_s does not depend upon apparent area of contact.

1. Static Frictional Force : Static friction is the friction that exists between a stationary object and the surface on which it resting. Static friction keeps an object at rest. It must is overcome to start moving the object.

Imagine trying to push an object across the floor. You push on it with a small force, but it does not move, this is because it is not accelerating. However, according to Newton’s second law, the object must move with an acceleration.
a = \(\frac{F}{m}\)
Now, as the body remains at rest, it implies that an opposing force equal to the applied force must have come into play resulting in zero net force on the object. This force is called static friction. It is denoted by F_s.

Thus, static friction is the opposing force that comes into play when one body tends to move over the surface of another, but the actual motion has not started.

• The static friction depends upon the nature of surfaces of the two bodies in contact.
• The static friction does not exist by itself. When there is no applied force, there is no static friction. It comes into play only when the applied force tends to move the body.
• he static friction is a self-adjusting force.

Limiting Friction : If the applied force is increased, the force of static friction also increases. If the applied force exceeds a certain (maximum) value, the body starts moving. This maximum value of static friction up to which the body does not move, is called limiting friction.

1. The magnitude of limiting- friction between any two bodies in contact is directly proportional to the normal reaction between them.
(f_s)_max ∝ N
(f_s) _max ∝ μ_s N ………….. (1)
Where the constant of proportionality p s is called the coefficient of static friction. Its value depends upon the nature of surfaces of the two bodies in contact that means whether dry or wet; rough or smooth; polished or non polished. For example, when two polished metal surfaces are in contact, ps = 0.2, when these surface are lubricated,

μ_s = 0.1
The value of μ_s lies between 0 and 1 or 0 < μ_s < 1
∵ N = Mg
(F_s)_max = μ_s m_g ……………… (2)

2. Direction of the force of limiting friction is always opposite to the direction in which one body is at the verge of moving over the other.

3. Coefficient of Static Friction :
μ_s is called coefficient of static friction and is defined as the ratio of force of limiting friction and normal reaction
From(1), μ_s = \(\frac{\left(f_{s}\right)_{\max }}{N}\)
Dimension: [M⁰L⁰T⁰]
Unit: It has no unit.
Value of μ_s does not depend upon apparent area of contact.

2. Kinetic Friction : We know that when the applied force on a body is small, it may not move but as the applied force becomes greater than the force of limiting friction, the body is set into motion. The force of friction acting between the two surfaces in contact which are moving relatively, so as to oppose their motion, is known as kinetic frictional force.
1. Kinetic friction is directly proportional to the normal reaction i. e.,
f_k ∝ N

or f_k ∝ μ_kN ………….. (1)
Where μ_k, is called the coefficient of kinetic friction.
∵ N – mg
∴ f_k = μ_kmg …………… (2)
2. Value of μ_k depends upon the nature of surface in contact.
3. Kinetic friction is always lesser than the limiting friction
f_k < (f_s)_max
∴ μ_k < μ_s

i. e., Coefficient of kinetic friction is always less than coefficient of static friction. Thus we require more force to start a motion than to maintain it against friction. This is because once the motion starts actually; inertia of rest has been over come. Also when motion has actually started, irregularities of one surface have little time to get locked again into the irregularities of the other surface.
4. Kinetic friction does not depend upon the velocity of the body.

μ_s > μ_k because f_s > f_k.

Static because f_s > f_k i. e., static friction is more than dynamic friction.

Radio signals are emitted by the planet Jupiter.

Winter season constellation is Orion.