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Concept:

We can use the equations of motion to find the speed of the ball at the ground.

The ball is subject to gravity, and as it falls, its speed increases.

The final speed depends on the initial speed, the distance fallen, and the acceleration due to gravity.

We use the equation of motion: v^₂ = u² + 2gh

Where:

• v is the final velocity (speed at the ground),
• u = 8 m/s is the initial velocity (speed at the top of the window),
• h = 1.8 m is the distance fallen from the top of the window to the ground,
• g = 9.8 m/s² is the acceleration due to gravity.

Calculation:

Here,

• Mass of the ball m = 0.5 kg (not needed for this calculation)
• Initial speed at the top of the window, v₁ = 8 m/s
• Height of the top of the window from the ground, h = 1.8 m
• Acceleration due to gravity g = 9.8 m/s²

^{\( v^2 = (8)^2 + 2 \times 9.8 \times 1.8 \)}

\( v^2 = 64 + 2 \times 9.8 \times 1.8 \)

v² = 64 + 35.28 

v² = 99.28 

Take the square root of both sides to find v,

\( v = \sqrt{99.28} \approx 9.96 , \text{m/s} \) (closer to 10m/s)

The correct answer is option (1).

Correct answer: 3)

Concept:

• The number of protons in the nucleus of the atom is equal to the atomic number (Z).
• The number of electrons in a neutral atom is equal to the number of protons.
• The mass number of the atom (M) is equal to the sum of the number of protons and neutrons in the nucleus.
• The number of neutrons is equal to the difference between the mass number of the atom (M) and the atomic number (Z).

Explanation:

The atomic number of tin is 50.

The number of protons is equal to the atomic number, hence protons = 50.

The number of protons is equal to the number of electrons in a neutral atom. but here in the Tin has 2+  charge, which means An has donated 2 electrons.

Hence, Sn2+ has 48 electrons in it.

Mass number = no. of protons + no. of neutrons

Hence, no. of neutrons = 119 - 50 = 69

Conclusion:

Thus, Sn2+ has 50 protons, 69 neutrons, and 48 electrons.

CONCEPT:

Formation of Ionic Compounds Based on Valence Electrons

• Atoms form ionic compounds by transferring electrons to achieve stable electronic configurations (usually an octet).
• The total positive and negative charges must balance in the compound.
• Metals (like atom T with 3 valence electrons) tend to lose electrons and form cations.
• Non-metals (like atom S with 6 valence electrons) tend to gain electrons and form anions.

EXPLANATION:

• Given:
• Atom T has 3 valence electrons → likely forms T³⁺ by losing 3 electrons.
• Atom S has 6 valence electrons → likely forms S²⁻ by gaining 2 electrons.
• To form a neutral compound, the total positive and negative charges must be equal.
• We find the least common multiple (LCM) of the charges 3 and 2, which is 6.
• So, to get +6 charge: use 2 T³⁺ ions → 2 × (+3) = +6
• To get −6 charge: use 3 S²⁻ ions → 3 × (−2) = −6
• Thus, the formula that balances the charges is T₂S₃.

Therefore, the correct formula of the ionic compound is T₂S₃.

Correct answer: 2)

Concept:

• Weight is the force of gravity on an object.
• Mass is a property of matter.
• Vacuum permittivity is defined as the vacuum's ability to permit an electric field or the capacity of the electric field to travel through a vacuum.

Explanation:

• There are three basic properties that describe an elementary particle: 'mass', 'charge', and 'spin'. Each property is assigned a number value.
• The permittivity of free space is a physical constant that reflects the ability of electrical fields to pass through a classical vacuum.
• Though the mass of an object remains constant, its weight varies according to its location.
• No matter how you measure it, the speed of light is always the same. The speed of light in free space is constant.

Conclusion:

Thus, the weight of an object is not a constant.

Concept:

Force on an object is given by

F = mg

where m is the mass of the object and g is the acceleration due to gravity.

Calculation:

Given:

Mass of a boy = 60 kg.

Weight of a school bag = 30 N.

F = mg.

Substituting the given values in the formula,

⇒ F = 60 × 10

⇒ F = 600 N

Now,

The total force exerted on the ground by a boy,

⇒ F = 600 + 30

⇒ F = 630 N

The correct answer is option (3).

Calculation:

Given that 

m = 120 kg, g = 10 m/s²,  A = 40 cm²

We know that 

F = ma

Therefore, weight

W = 120 kg ×  10 m/s² = 1200 N

Now, 

Pressure = Force / Area

Pressure = 1200/(40 × 10^-4)

Pressure = 3 × 10⁵ N/m²

Concept:

Force acting on the object is given by

F = mg

where m is the mass and g is the acceleration due to gravity.

Calculation:

F₂ = mg

= 2000 × 10

= 20000 N

Area = 30x = 30 × 30 cm² = 900 × 10^-4 m²

\({F_1\over A_1} = {F_2 \over A_2}\)

F₁ = \({F_2 \times A_1 \over A_2}\)

= \({20000\times 9 × 10^{-4}\over 900 × 10^{-4}}\)

= 200 N

The correct answer is option (1).

Concept:

The relative density of metal in this case is given by,

RD = \(\text{weight in the air }\over \text{change in weight in water}\)

Calculation:

The relative density of metal in this case is given by

RD = \({0.096 \over 0.096 - 0.064}\)

= 3

The density of metal = RD × ρ 

= 3 × 10³  kg/m³

The correct answer is option (3).

Correct answer: 1)

Concept:

• Atoms with the same number of protons but different numbers of neutrons are called isotopes.
• They share almost the same chemical properties, but differ in mass and therefore in physical properties.

Explanation:

• Carbon occurs naturally in three isotopes: carbon 12, which has 6 neutrons (plus 6 protons equals 12), carbon 13, which has 7 neutrons, and carbon 14, which has 8 neutrons.
• Every element has its own number of isotopes.
• So, isotopes of carbon differ by atomic mass.

Conclusion:

Thus, there are two stable isotopes of Carbon. They differ with respect to atomic mass.

Correct answer: 3)

Concept:

• The Law of Conservation of Mass dates from Antoine Lavoisier's 1789 discovery that mass is neither created nor destroyed in chemical reactions.
• In other words, the mass of any one element at the beginning of a reaction will equal the mass of that element at the end of the reaction.

Explanation:

• Since chemical reactions are just the rearrangement of the atomic bonds between the forming atoms in a substance, they are not created nor destroyed in this process.
• This rearrangement changes the physical and chemical properties of the substance but the number of atoms keeps constant in that system. Since the mass of the atoms does not change, the mass of the reactants and the products is the same.

Conclusion:

 Thus, the mass of the sealed flask after heating will be 140 g.