# Gravitation - Class 9 - Science

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## Back Questions - Gravitation | NCERT | Science | Class 9

How does the force of gravitation between two objects change when the distance between them is reduced to half?

The force of gravitation between two objects is given by Newton's law of universal gravitation, which states that the gravitational force ($F$) between two masses ($m_1$ and $m_2$) is directly proportional to the product of their masses and inversely proportional to the square of the distance ($r$) between their centers:

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

where $G$ is the gravitational constant.

If the distance between two objects is reduced to half, the new distance between them is $\frac{r}{2}$. Plugging this into the equation, we get:

$$ F' = G \cdot \frac{m_1 \cdot m_2}{\left(\frac{r}{2}\right)^2} = G \cdot \frac{m_1 \cdot m_2}{\frac{r^2}{4}} = 4 \cdot G \cdot \frac{m_1 \cdot m_2}{r^2}$$

Comparing the new force ($F'$) to the original force ($F$):

$$ F' = 4 \cdot F $$

This means that the gravitational force becomes four times stronger when the distance between two objects is reduced to half.

Gravitational force acts on all objects in proportion to their masses. Why then, a heavy object does not fall faster than a light object?

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Sign up nowWhat is the magnitude of the gravitational force between the earth and a $1 \mathrm{~kg}$ object on its surface? (Mass of the earth is $6 \times 10^{24} \mathrm{~kg}$ and radius of the earth is $6.4 \times 10^{6} \mathrm{~m}$.

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Sign up nowThe earth and the moon are attracted to each other by gravitational force. Does the earth attract the moon with a force that is greater or smaller or the same as the force with which the moon attracts the earth? Why?

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Sign up nowIf the moon attracts the earth, why does the earth not move towards the moon?

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What happens to the force between two objects, if

(i) the mass of one object is doubled?

(ii) the distance between the objects is doubled and tripled?

(iii) the masses of both objects are doubled?

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What is the importance of universal law of gravitation?

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What is the acceleration of free fall?

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What do we call the gravitational force between the earth and an object?

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Amit buys few grams of gold at the poles as per the instruction of one of his friends. He hands over the same when he meets him at the equator. Will the friend agree with the weight of gold bought? If not, why? [Hint: The value of $g$ is greater at the poles than at the equator.]

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Why will a sheet of paper fall slower than one that is crumpled into a ball?

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Gravitational force on the surface of the moon is only $\frac{1}{6}$ as strong as gravitational force on the earth. What is the weight in newtons of a $10 \mathrm{~kg}$ object on the moon and on the earth?

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A ball is thrown vertically upwards with a velocity of $49 \mathrm{~m} / \mathrm{s}$. Calculate

(i) the maximum height to which it rises,

(ii) the total time it takes to return to the surface of the earth.

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A stone is released from the top of a tower of height $19.6 \mathrm{~m}$. Calculate its final velocity just before touching the ground.

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A stone is thrown vertically upward with an initial velocity of $40 \mathrm{~m} / \mathrm{s}$. Taking $g=10 \mathrm{~m} / \mathrm{s}^{2}$, find the maximum height reached by the stone. What is the net displacement and the total distance covered by the stone?

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Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth $=6 \times 10^{24} \mathrm{~kg}$ and of the Sun $=2 \times 10^{30} \mathrm{~kg}$. The average distance between the two is $1.5 \times 10^{11} \mathrm{~m}$.

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A stone is allowed to fall from the top of a tower $100 \mathrm{~m}$ high and at the same time another stone is projected vertically upwards from the ground with a velocity of $25 \mathrm{~m} / \mathrm{s}$. Calculate when and where the two stones will meet.

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A ball thrown up vertically returns to the thrower after $6 \mathrm{~s}$. Find

(a) the velocity with which it was thrown up,

(b) the maximum height it reaches, and

(c) its position after $4 \mathrm{~s}$.

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In what direction does the buoyant force on an object immersed in a liquid act?

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Why does a block of plastic released under water come up to the surface of water?

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The volume of $50 \mathrm{~g}$ of a substance is $20 \mathrm{~cm}^{3}$. If the density of water is $1 \mathrm{~g} \mathrm{~cm}^{-3}$, will the substance float or sink?

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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?