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## Class 9 - Gravitation

1. State the universal law of gravitation Ans. The universal law of gravitation states that every object in the universe attracts every other object with a force called the gravitational force. The force acting between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. For two objects of masses $$m_1$$ and $$m_2$$ and the distance between them $$r$$, the force $$(F)$$ of attraction acting between them is given by the universal law of gravitation as:

F=\frac{G m_1 m_2}{r^2}

Where, \mathrm{G} is the universal gravitation constant given by: $$G=6.67 \times 10^{-11} \mathrm{Nm}^2 / \mathrm{kg}^2$$

2. Write the formula to find the magnitude of the gravitational force between the earth and an object on the surface of the earth.

Ans. Let $$M_{\mathrm{E}}$$ be the mass of the Earth and $$m$$ be the mass of an object on its surface. If $$R$$ is the radius of the Earth, then according to the universal law of gravitation, the gravitational force $$(F)$$ acting between the Earth and the object is given by the relation:

$$F=\frac{G m_1 m_2}{r^2}$$

1. What do you mean by free fall?
Ans. Gravity of the Earth attracts every object towards its centre. When an object is released from a height, it falls towards the surface of the Earth under the influence of gravitational force. The motion of the object is said to have free fall.
2. What do you mean by acceleration due to gravity?
Ans. When an object falls towards the ground from a height, then its velocity changes during the fall. This changing velocity produces acceleration in the object. This acceleration is known as acceleration due to gravity $$(g)$$. Its value is given by $$9.8 \mathrm{m} / \mathrm{s}^2$$.
1. What are the differences between the mass of an object and its weight?
Ans.
\begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|}{ Mass } & \multicolumn{1}{c|}{ Weight } \\
\hline Mass is the quantity of matter contained in the body. & Weight is the force of gravity acting on the body. \\
\hline It is the measure of inertia of the body. & It is the measure of gravity. \\
\hline Mass is a constant quantity. & Weight is not a constant quantity. It is different at different places. \\
\hline It only has magnitude. & It has magnitude as well as direction. \\
\hline Its SI unit is kilogram $$(\mathrm{kg})$$. & Its SI unit is the same as the SI unit of force, i.e., Newton (N). \\
\hline
\end{tabular}
2. Why is the weight of an object on the moon $$\frac{1}{6}$$ its weight on the earth?
Ans. Let $$M_{\mathrm{E}}$$ be the mass of the Earth and $$m$$ be an object on the surface of the Earth. Let $$R_{\mathrm{E}}$$ be the radius of the Earth. According to the universal law of gravitation, weight $$W_{\mathrm{E}}$$ of the object on the surface of the Earth is given by,
$$W_E=\frac{G M_E m}{R_E{ }^2}$$
Let $$\mathrm{M}_{\mathrm{M}}$$ and $$\mathrm{R}_{\mathrm{M}}$$ be the mass and radius of the moon. Then, according to the universal law of gravitation, weight $$W_{\mathrm{M}}$$ of the object on the surface of the moon is given by:
\begin{aligned} &W_M=\frac{G M_M m}{R_M{ }^2} \\ &\frac{W_M}{W_E}=\frac{\frac{G M_M m}{R_M{ }^2}}{\frac{G M_E m}{R_E{ }^2}}=\frac{M_M R_E{ }^2}{M_E R_M{ }^2} \\ &\text { where, } M_E=5.98 \times 10^{24} \mathrm{kg}, M_M=7.36 \times 10^{22} \mathrm{kg} \\ &R_E=6.4 \times 10^6 \mathrm{m}, R_M=1.74 \times 10^6 \mathrm{m} \\ &\frac{W_M}{W_E}=\frac{7.36 \times 10^{22} \times\left(6.4 \times 10^6\right)^2}{5.98 \times 10^{24} \times\left(1.74 \times 10^6\right)^2}=0.165 \approx \frac{1}{6} \end{aligned}
Therefore, the weight of an object on the moon $$\frac{1^{\text {th }}}{6}$$ its weight on the earth

1. Why is it difficult to hold a school bag having a strap made of a thin and strong string? Ans.: It is difficult to hold a school bag having a thin strap because the pressure on the shoulders is quite large. This is because the pressure is inversely proportional to the surface area on which the force acts. The smaller is the surface area; the larger will be the pressure on the surface. In the case of a thin strap, the contact surface area is very small. Hence, the pressure exerted on the shoulder is very large.
2. What do you mean by buoyancy?
Ans.: The upward force exerted by a liquid on an object immersed in it is known as buoyancy. When you try to immerse an object in water, then you can feel an upward force exerted on the object, which increases as you push the object deeper into water..
3. Why does an object float or sink when placed on the surface of water?
Ans.: If the density of an object is more than the density of the liquid, then it sinks in the liquid. This is because the buoyant force acting on the object is less than the force of gravity. On the other hand, if the density of the object is less than the density of the liquid, then it floats on the surface of the liquid. This is because the buoyant force acting on the object is greater than the force of gravity.

1. You find your mass to be $$42 \mathrm{kg}$$ on a weighing machine. Is your mass more or less than $$42 \mathrm{kg}$$ ?
Ans.: When you weigh your body, an upward force acts on it. This upward force is the buoyant force. As a result, the body gets pushed slightly upwards, causing the weighing machine to show a reading less than the actual value.
2. You have a bag of cotton and an iron bar, each indicating a mass of $$100 \mathrm{kg}$$ when measured on a weighing machine. In reality, one is heavier than other. Can you say which one is heavier and why?
Ans.: The iron bar is heavier than the bag of cotton. This is because the surface area of the cotton bag is larger than the iron bar. Hence, more buoyant force acts on the bag than that on an iron bar. This makes the cotton bag lighter than its actual value. For this reason, the iron bar and the bag of cotton show the same mass on the weighing machine, but actually the mass of the iron bar is more that that of the cotton bag.
19. In what direction does the buoyant force on an object immersed in a liquid act? An object immersed in a liquid experiences buoyant force in the upward direction.
20. Why does a block of plastic released under water come up to the surface of water? Two forces act on an object immersed in water. One is the gravitational force, which pulls the object downwards, and the other is the buoyant force, which pushes the object upwards. If the upward buoyant force is greater than the downward gravitational force, then the object comes up to the surface of the water as soon as it is released within water. Due to this reason, a block of plastic released under water comes up to the surface of the water.
21. The volume of $$50 \mathrm{g}$$ of a substance is $$20 \mathrm{cm} 3$$. If the density of water is $$1 \mathrm{gcm}^{-3}$$, will the substance float or sink?
If the density of an object is more than the density of a liquid, then it sinks in the liquid. On the other hand, if the density of an object is less than the density of a liquid, then it floats on the surface of the liquid.
Here, density of the substance $$=\frac{\text { Mass of the substance }}{\text { Volume of the substance }}=\frac{50}{20}=2.5 \mathrm{g} / \mathrm{cm}^3$$
The density of the substance is more than the density of water $$(1 \mathrm{g} \mathrm{cm}-3)$$. Hence, the substance will sink in water.
22. The volume of a $$500 \mathrm{g}$$ sealed packet is $$350 \mathrm{cm}^3$$. Will the packet float or sink in water if the density of water is $$1 \mathrm{g} \mathrm{cm}^{-3}$$ ? What will be the mass of the water displaced by this packet?
Density of the $$500 \mathrm{g}$$ sealed packet $$=\frac{\text { Mass of the packet }}{\text { Volume of the packet }}=\frac{500}{350}=1.428 \mathrm{g} / \mathrm{cm}^3$$
The density of the substance is more than the density of water $$\left(1 \mathrm{g} / \mathrm{cm}^3\right)$$. Hence, it will sink in water.
The mass of water displaced by the packet is equal to the volume of the packet, i.e., $$350 \mathrm{g}$$.

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