1. The derived unit from the options given is Newton (C). Derived units are combinations of the seven base units. For example, Newton is a derived unit of force in the International System of Units, expressed as m·kg·s⁻².

2. The standard unit of electric current is Ampere (B). It is one of the seven base units in the International System of Units.

3. The volume of a cube is given by the formula V = a³, where a is the length of one side. If the volume V is 125 cm³, then the length of one side a is the cube root of 125, which is 5 cm (A).

4. The scalar quantity from the options given is Mass (C). Scalar quantities have magnitude only, while vector quantities have both magnitude and direction.

5. The dimensional formula of Planck's constant (h) is [ML²T⁻¹] (A). This can be derived from the formula E = hf, where E is energy (dimensions [ML²T⁻²]), f is frequency (dimensions T⁻¹), and h is Planck's constant.

Section B:

1. Precision refers to the closeness of two or more measurements to each other, while accuracy refers to how close a measured value is to the actual (true) value.

2. Average speed is calculated by dividing the total distance travelled by the total time taken. So, 240 km divided by 4 hours gives an average speed of 60 km/h.

3. To convert from m³ to cm³, multiply by 1,000,000 (since 1 m = 100 cm, and (100 cm)³ = 1,000,000 cm³). So, 2.5 m³ is 2,500,000 cm³.

4. A vernier caliper is more accurate than a simple meter scale because it can measure to a higher precision, typically to the nearest 0.01 cm, due to the additional vernier scale.

5. Density is calculated by dividing mass by volume. So, 20 kg divided by 4 m³ gives a density of 5 kg/m³.

Section C:

1. (a) The vernier caliper works on the principle of using a main scale and a sliding vernier scale to measure lengths more precisely than a simple ruler. The difference between the scales gives the precise measurement. (b) The measured length is the sum of the main scale reading and the vernier scale reading, so 2.3 cm + 0.07 cm = 2.37 cm.

2. (a) One light year is the distance that light travels in one year in a vacuum, approximately 9.461 trillion kilometers. (b) To find the distance to Proxima Centauri in kilometers, multiply the distance in light years by the number of kilometers in a light year, so 4.22 light years is approximately 4.22 * 9.461 trillion kilometers = 39.925 trillion kilometers.

3. (a) Newton's three laws of motion are: (i) An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force (Law of Inertia). (ii) Force is equal to the change in momentum per change in time (F = ma). (iii) For every action, there is an equal and opposite reaction. (b) The acceleration of the object is calculated by dividing the force by the mass, so 50 N divided by 10 kg gives an acceleration of 5 m/s².

4. (a) Scalars are quantities that have magnitude only, such as mass or temperature. Vectors have both magnitude and direction, such as velocity or force. (b) The total displacement of the car is the vector sum of the two displacements, which can be calculated using the Pythagorean theorem to give a displacement of sqrt((150 km)² + (200 km)²) = 250 km.

5. (a) Dimensional analysis is a method used in physics to check the correctness of equations and to derive relationships between physical quantities. It is based on the principle that every physical quantity

Question

1. The derived unit from the options given is Newton (C). Derived units are combinations of the seven base units. For example, Newton is a derived unit of force in the International System of Units, expressed as m·kg·s⁻².

2. The standard unit of electric current is Ampere (B). It is one of the seven base units in the International System of Units.

3. The volume of a cube is given by the formula V = a³, where a is the length of one side. If the volume V is 125 cm³, then the length of one side a is the cube root of 125, which is 5 cm (A).

4. The scalar quantity from the options given is Mass (C). Scalar quantities have magnitude only, while vector quantities have both magnitude and direction.

5. The dimensional formula of Planck's constant (h) is [ML²T⁻¹] (A). This can be derived from the formula E = hf, where E is energy (dimensions [ML²T⁻²]), f is frequency (dimensions T⁻¹), and h is Planck's constant.

Section B:

1. Precision refers to the closeness of two or more measurements to each other, while accuracy refers to how close a measured value is to the actual (true) value.

2. Average speed is calculated by dividing the total distance travelled by the total time taken. So, 240 km divided by 4 hours gives an average speed of 60 km/h.

3. To convert from m³ to cm³, multiply by 1,000,000 (since 1 m = 100 cm, and (100 cm)³ = 1,000,000 cm³). So, 2.5 m³ is 2,500,000 cm³.

4. A vernier caliper is more accurate than a simple meter scale because it can measure to a higher precision, typically to the nearest 0.01 cm, due to the additional vernier scale.

5. Density is calculated by dividing mass by volume. So, 20 kg divided by 4 m³ gives a density of 5 kg/m³.

Section C:

1. (a) The vernier caliper works on the principle of using a main scale and a sliding vernier scale to measure lengths more precisely than a simple ruler. The difference between the scales gives the precise measurement. (b) The measured length is the sum of the main scale reading and the vernier scale reading, so 2.3 cm + 0.07 cm = 2.37 cm.

2. (a) One light year is the distance that light travels in one year in a vacuum, approximately 9.461 trillion kilometers. (b) To find the distance to Proxima Centauri in kilometers, multiply the distance in light years by the number of kilometers in a light year, so 4.22 light years is approximately 4.22 * 9.461 trillion kilometers = 39.925 trillion kilometers.

3. (a) Newton's three laws of motion are: (i) An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force (Law of Inertia). (ii) Force is equal to the change in momentum per change in time (F = ma). (iii) For every action, there is an equal and opposite reaction. (b) The acceleration of the object is calculated by dividing the force by the mass, so 50 N divided by 10 kg gives an acceleration of 5 m/s².

4. (a) Scalars are quantities that have magnitude only, such as mass or temperature. Vectors have both magnitude and direction, such as velocity or force. (b) The total displacement of the car is the vector sum of the two displacements, which can be calculated using the Pythagorean theorem to give a displacement of sqrt((150 km)² + (200 km)²) = 250 km.

5. (a) Dimensional analysis is a method used in physics to check the correctness of equations and to derive relationships between physical quantities. It is based on the principle that every physical quantity

Knowee AI · Accepted Answer

1. The derived unit from the options given is Newton (C). Derived units are combinations of the seven base units. For example, Newton is a derived unit of force in the International System of Units, expressed as m·kg·s⁻².

2. The standard unit of electric current is Ampere (B). It is one of the seven base units in the International System of Units.

3. The volume of a cube is given by the formula V = a³, where a is the length of one side. If the volume V is 125 cm³, then the length of one side a is the cube root of 125, which is 5 cm (A).

4. The scalar quantity from the options given is Mass (C). Scalar quantities have magnitude only, while vector quantities have both magnitude and direction.

5. The dimensional formula of Planck's constant (h) is [ML²T⁻¹] (A). This can be derived from the formula E = hf, where E is energy (dimensions [ML²T⁻²]), f is frequency (dimensions T⁻¹), and h is Planck's constant.

Section B:

1. Precision refers to the closeness of two or more measurements to each other, while accuracy refers to how close a measured value is to the actual (true) value.

2. Average speed is calculated by dividing the total distance travelled by the total time taken. So, 240 km divided by 4 hours gives an average speed of 60 km/h.

3. To convert from m³ to cm³, multiply by 1,000,000 (since 1 m = 100 cm, and (100 cm)³ = 1,000,000 cm³). So, 2.5 m³ is 2,500,000 cm³.

4. A vernier caliper is more accurate than a simple meter scale because it can measure to a higher precision, typically to the nearest 0.01 cm, due to the additional vernier scale.

5. Density is calculated by dividing mass by volume. So, 20 kg divided by 4 m³ gives a density of 5 kg/m³.

Section C:

1. (a) The vernier caliper works on the principle of using a main scale and a sliding vernier scale to measure lengths more precisely than a simple ruler. The difference between the scales gives the precise measurement. (b) The measured length is the sum of the main scale reading and the vernier scale reading, so 2.3 cm + 0.07 cm = 2.37 cm.

2. (a) One light year is the distance that light travels in one year in a vacuum, approximately 9.461 trillion kilometers. (b) To find the distance to Proxima Centauri in kilometers, multiply the distance in light years by the number of kilometers in a light year, so 4.22 light years is approximately 4.22 * 9.461 trillion kilometers = 39.925 trillion kilometers.

3. (a) Newton's three laws of motion are: (i) An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force (Law of Inertia). (ii) Force is equal to the change in momentum per change in time (F = ma). (iii) For every action, there is an equal and opposite reaction. (b) The acceleration of the object is calculated by dividing the force by the mass, so 50 N divided by 10 kg gives an acceleration of 5 m/s².

4. (a) Scalars are quantities that have magnitude only, such as mass or temperature. Vectors have both magnitude and direction, such as velocity or force. (b) The total displacement of the car is the vector sum of the two displacements, which can be calculated using the Pythagorean theorem to give a displacement of sqrt((150 km)² + (200 km)²) = 250 km.

5. (a) Dimensional analysis is a method used in physics to check the correctness of equations and to derive relationships between physical quantities. It is based on the principle that every physical quantity

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