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The correct answer is Amplitude.

Key Points

• The softness of a sound is determined basically by its amplitude.
• The amplitude of the sound wave depends upon the force with which an object is made to vibrate.

 Additional Information

• Phase specifies the location or timing of a point within a wave cycle of a repetitive waveform.
• A time period (denoted by 'T') is the time taken for one complete cycle of vibration to pass a given point.
• Oscillation is defined as the process of repeating variations of any quantity or measure about its equilibrium value in time.

The correct answer is Conservation of energy.

Key Points

• The conservation of energy is a fundamental principle in physics, stating that the total energy of an isolated system remains constant over time.
• This principle implies that energy can neither be created nor destroyed, but it can be transformed from one form to another.
• Energy transformation examples include converting kinetic energy to thermal energy or potential energy to kinetic energy.
• The conservation of energy is a cornerstone of classical mechanics, thermodynamics, and quantum mechanics.
• This law is crucial for understanding a wide range of physical phenomena and engineering applications, from the motion of planets to the functioning of engines.

 Additional Information

• Conservation of momentum
• The conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it.
• This principle is essential in collision analysis and rocket propulsion.
• Conservation of mass
• The conservation of mass states that mass in an isolated system is neither created nor destroyed by chemical reactions or physical transformations.
• It is a fundamental concept in chemistry and fluid dynamics.
• Conservation of mechanical energy
• The conservation of mechanical energy is a specific case of the conservation of energy, applicable when only conservative forces are acting.
• It states that the sum of kinetic and potential energy remains constant in an isolated system.

Concept:

Kinematics is the study of the motion of a system of bodies without directly considering the forces or potential fields affecting the motion.

Calculation:

Apply the equation of kinematic

v = u + at

Acceleration, 

a = \({v-u \over t}\)

= \({5 \over 5 \times 10^{-4}}\)

Force = mass × acceleration

= 4 × 10⁴ N.

The correct answer is option (4).

Correct answer: 1)

Concept:

• Allotropes of carbon are diamond, graphite, and buckminsterfullerene.
• The physical properties of these allotropes vary with their form.
• Carbon has an oxidation state of +4 as it is tetravalent and can form four covalent bonds.
• In carbon monoxide and in carbonyl complexes, the oxidation state of carbon is +2.
• Hence, the atomic mass of carbon is 12 g/mol.

Explanation:

• Natural carbon is formed by 98.93% of isotope C-12 with a mass of 12.01115 units, and 1.07% of isotope C-13 with a mass of 13.003355 units.
• Mass of one atom of carbon−14 is  14.0032420u.
• 14.00324 u is not possible for carbon atoms.

Conclusion:

Thus, The impossible mass of a Carbon atom is 12.00000 u.

Correct answer: 1)

Concept:

• A decomposition reaction occurs when one reactant breaks down into two or more products. This can be represented by the general equation: AB → A + B.
• The speed at which the decomposition occurs called the "rate of decomposition", depends on the temperature, moisture, and chemical composition of the organic matter.

Explanation:

• The decomposition of  Cl2O7, to form Cl2 and O2
• 2Cl2O7,→ 2Cl₂ +7O₂
• So the ratio of chlorine to oxygen will be 2:7.

Conclusion:

Thus, the ratio of Chlorine to Oxygen molecules in the product is 2:7.

Correct answer: 1)

Concept:

• In Rutherford's alpha scattering experiment, when we pass the alpha particle on gold foil there are a few observations which are recorded as;
• Most of the particles remain undeflected
• Some of the particles are deflected through a small angle.
• Very few particles are deflected by 1800 and came back

Explanation:

From Rutherford's alpha scattering experiment, it is concluded that:

• Atom has most space as empty.
• A very small mass is concentrated in a small area called a nucleus.
• The mass of an atom is concentrated at the central nucleus and the remaining part is empty.
• Therefore, when sent through the metal foil, the positively charged alpha particles go straight through the foil.

Conclusion:

Thus, the scattering of α-particles by thin metal foils establishes that the mass and positive charge of an atom are concentrated in a nucleus.

Concept:

• Displacement is the change in position of an object.
• SI unit is meter(m).
• The slope of displacement - time graph gives velocity.
• The area under the velocity-time graph gives displacement and the area under the acceleration - time graph gives the change in velocity.
• Velocity: The rate of change of displacement of a body is called the velocity of that body.
• Velocity is a vector quantity that has both magnitudes as well as directions.
• Acceleration: The rate of change of velocity is called the acceleration of the body.
• Acceleration is also a vector quantity.
• The slope of any velocity-time graph gives an acceleration of the body.
• Distance: The total path length between two points is called distance.

Explanation:

• Displacement time graph is the plot of motion of an object (s - Y-axis) against time (t - X-axis).
• Graph 3) is represents a diagonally straight line which means that the object is in uniform motion with time.
• Graphs 2) and 4) represent the non-uniform motion of the object, while a horizontal line parallel to the X axis shows that there is no motion in the object with time.

⇒ there is no change in position with respect to time, object is at rest.

∴ The correct answer is option 1)

Concept:

Energy is always conserved. Hence work done equals a change in potential energy.

Calculation:

W = mg(h₂ - h₁)

W = 2 × 10 × (10 - 1)

W = 180 J

Given:

Initial speed of the first bullet, u₁ = 160 m/s

Final speed of the first bullet, v₁ = 140 m/s

Initial speed of the second bullet, u₂ = 60 m/s

Formula Used:

Change in speed for the first bullet:

Δv₁ = u₁ - v₁

Change in speed for the second bullet:

Δv₂ = u₂ - v₂

Since the resistance is the same for both bullets, Δv₁ = Δv₂

Calculation:

We have,

⇒ Δv₁ = 160 - 140 = 20 m/s

For the second bullet,

⇒ Δv₂ = Δv₁

⇒ Δv₂ = 20 m/s

The final speed of the second bullet, v₂

⇒ v₂ = u₂ - Δv₂

⇒ v₂ = 60 m/s - 20 m/s

⇒ v₂ = 40 m/s

∴ The second bullet's speed after passing through plank is equal to 40 m/s.

Concept:

• The Law of Conservation of Energy states that the total energy of an isolated system remains conserved (constant), that is, it can neither be created nor be destroyed but it can be transformed from one form to another
• Energy always transforms from one form to another in this case energy is been transformed in the following order
• Potential energy is converted to kinetic energy & heat produce because of air resistance as it falls and as it hits the ground it been wasted as sound and heat energy.
• One of the most common examples of the Law of Conservation of Energy is: water is stored at a height with some potential energy, when the water starts flowing downward then its potential energy is converted into kinetic energy.
• \(Kinetic;Energy = \frac{1}{2}m{v^2}\)
• \(Potential;Energy = mgh\)

Change in Gravitational potential energy = Kinetic Energy.

Calculation:

Initial Kinetic Energy

\(KE_{\text{initial}} = \frac{1}{2} \cdot m \cdot u^2\)

\(KE_{\text{initial}} = \frac{1}{2} \cdot 0.2 \cdot 20^2 = 40 , J\)

Potential Energy at the Top

\(PE = m \cdot g \cdot h\)

\(PE = 0.2 \cdot 10 \cdot 15 = 30 , J\)

Total Kinetic Energy at the River Level

When the stone hits the river, the total kinetic energy is:

\(KE_{\text{total}} = KE_{\text{initial}} + PE\)

\(KE_{\text{total}} = 40 , J + 30 , J = 70 , J\)

∴ The kinetic energy of the stone when it lands in the river is 70 J