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Gravitation - Mass and Weight

Grade 9CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Mass is the measure of the quantity of matter contained in an object. It is a scalar quantity and its SI unit is kgkg.

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Mass of an object is constant and does not change from place to place. It is also a measure of the inertia of an object.

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Weight is the force with which an object is attracted towards the Earth. It is a vector quantity and its SI unit is Newton (NN).

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The weight of an object depends on its location because the acceleration due to gravity (gg) varies from place to place (W=m×gW = m \times g).

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On the surface of the Earth, the value of gg is approximately 9.8 m/s29.8 \text{ m/s}^2.

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The weight of an object on the Moon is approximately 16\frac{1}{6} of its weight on the Earth because the Moon's gravitational pull is weaker due to its smaller mass and radius.

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Mass is measured using a beam balance, while weight is measured using a spring balance.

📐Formulae

W=m×gW = m \times g

g=G×MR2g = \frac{G \times M}{R^2}

Wmoon=16×WearthW_{moon} = \frac{1}{6} \times W_{earth}

1 kg-wt=9.8 N1 \text{ kg-wt} = 9.8 \text{ N}

💡Examples

Problem 1:

Mass of an object is 10 kg10 \text{ kg}. What is its weight on the Earth?

Solution:

W=m×gW = m \times g W=10 kg×9.8 m/s2=98 NW = 10 \text{ kg} \times 9.8 \text{ m/s}^2 = 98 \text{ N}

Explanation:

To find the weight, we multiply the mass of the object by the acceleration due to gravity on Earth (g≈9.8 m/s2g \approx 9.8 \text{ m/s}^2).

Problem 2:

An object weighs 60 N60 \text{ N} when measured on the surface of the Earth. What would be its weight when measured on the surface of the Moon?

Solution:

Wmoon=16×WearthW_{moon} = \frac{1}{6} \times W_{earth} Wmoon=16×60 N=10 NW_{moon} = \frac{1}{6} \times 60 \text{ N} = 10 \text{ N}

Explanation:

The acceleration due to gravity on the Moon is 16th\frac{1}{6}^{th} of that on the Earth, so the weight of any object becomes 16\frac{1}{6} of its weight on Earth.

Problem 3:

If the mass of a body is 30 kg30 \text{ kg} on Earth, what will be its mass and weight on the Moon? (Take g=9.8 m/s2g = 9.8 \text{ m/s}^2)

Solution:

Mass on Moon =30 kg= 30 \text{ kg}. Weight on Moon: Wmoon=16×(m×gearth)W_{moon} = \frac{1}{6} \times (m \times g_{earth}) Wmoon=16×(30 kg×9.8 m/s2)=49 NW_{moon} = \frac{1}{6} \times (30 \text{ kg} \times 9.8 \text{ m/s}^2) = 49 \text{ N}

Explanation:

Mass remains constant everywhere in the universe. However, weight changes based on the local acceleration due to gravity. The weight on the Moon is calculated by taking one-sixth of the weight on Earth.