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**Q.1.** **State the universal law of gravitation.****Ans.** Everybody in this universe attracts every other body with a force, which is directly proportional to the product of their masses and inversely proportional to the square of distance between their centres.

Universal Law of Gravitation**Q.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 mass of earth = M

mass of object = m.

If radius of the object is comparatively negligible, r ≈ radius of earth = R**F = GMm/R**^{2}

**Q.1. What do you mean by free fall?****Ans.** When an object falls with a constant acceleration, under the influence of force of gravitation of the earth, object is said to have free fall.**Q.2. What do you mean by acceleration due to gravity?****Ans.** During the course of its free fall, a body accelerates due to the force of gravity acting on it. This acceleration is known as acceleration due to gravity.

**Q.1. What are the differences between the mass of an object and its weight?**

**Ans.**

**Q.2. Why is the weight of an object on the moon 1/6th its weight on the earth?****Ans.**

► Mass of the moon (M) = 7.4 × 10^{22} kg

► Radius of the moon (R) = 1.74 × 10^{6} m

► Gravitational constant (G) = 6.7 × 10^{11} Nm^{2}kg^{2}

We know that acceleration due to gravity(g) =

► Also, weight , W = mg

► W =

Let the mass of the object be m, Let's its weight of moon be M_{m }and_{ }its radius be R_{m}

__By applying the universal law of gravitation, the weight of the object on the moon will be:__

(1)

Let the weight of the same object on the earth be We. The mass of earth is M and its radius is R.

(2)

__Substituting the values in equations (1) and (2) we get:__

W

and W

__On dividing and we get:__

∴ Weight of the object on the moon = its weight on earth

**Q.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.

**Q.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.

**Q.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.

**Q.1. You find your mass to be 42 kg on a weighing machine. Is your mass more or less than 42 kg? ****Ans. **Mass is always a constant quantity. Therefore, it cannot be more or less than 42 kg.**Q.2. You have a bag of cotton and an iron bar, each indicating a mass of 100 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 correct answer is cotton bag is heavier than iron bar.__The reason is:__

True weight = (apparent weight + up thrust)

- The density of cotton bag is less than that of the iron bar, so the volume of cotton bag is more compared to iron bar. So the cotton bag experience more upthrust due to the presence of air.
- Therefore in the presence of air, the true weight of cotton bag is more compared to the true weight of iron bar.

**Q.1. ****How does the force of gravitation between two objects change when the distance between them is reduced to half?Ans. **

F = (G m

When the distance between them is reduced to half, the gravitational force.

F' = (G m_{1}m_{2})/r^{2}

= (G m_{1}m_{2})/ (r/2)^{2}

= (4 G m_{1}m_{2})/(r^{2}) = 4F

The gravitational force becomes four times.**Q.2. ****Gravitational force acts on all objects in proportion to their masses. Why then, a heavy object does not fall faster than a light object?Ans.** The acceleration due to gravity of a freely falling body is independent of the mass of falling body. Thus, both heavy and light object fall with same acceleration.

Ans.

Mass of the object, m = 1 kg, radius of the earth, R = 6.4 x 10

Force of gravitation between them,

Ans.

- Earth attracts the moon with an equal and opposite force as moon attracts the earth.
- This is in accordance with Newton’s law of gravitation according to which gravitational force is the mutual force of attraction which is also equal as per to the third law of motion.

**Q.5. If the moon attracts the earth, why does the earth not move towards the moon? ****Ans.**

- The moon revolves around the earth because gravitation force of earth on moon provides the necessary centripetal force for circular motion.
- The moon also attracts the earth, due to which earth also revolves around the moon in circular orbit, but due to very large mass of earth, the motion of earth is not observed.
- It may be kept in mind that there is no linear motion of earth towards moon or moon towards earth. The gravitational force between them keeps on changing the direction of motion of moon or earth in circular orbit.

**Q.6. What happens to the force between two objects, if **

(a) the mass of one object is doubled?

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

(c) the masses of both objects are doubled? **Ans.** Let masses = m_{1} and m_{2}, distance between masses = r.

According to universal law of gravitation F ∝ m_{1}m_{2} and F ∝ 1/r_{2}.**(a)** If one mass, say m_{1} is doubled, and F ∝ m_{1}, then F gets doubled.**(b)** If distance is doubled and F ∝ 1/r^{2}, force becomes one-fourth, i.e. 1/(2)^{2}.

If distance is tripled and F ∝ 1/r^{2}, force becomes one-ninth, i.e. 1/(3)^{2}.**(c)** If both masses are doubled and F ∝ m_{1}m_{2}, force becomes 4 times, i.e. (2m_{1})(2m_{2}) = 4m_{1}m_{2} **Q.7. What is the importance of universal law of gravitation? ****Ans.**__Universal law of gravitation has successfully explained the phenomena which were earlier considered to be separate:__**(a)** It explains about the force which holds us on earth.**(b)** It explains the motion of planets around the sun.**(c)** It explains the motion of moon around the earth.**(d)** It explains about occurrence of tides in the ocean.**Q.8. What is the acceleration of free fall?****Ans.** When a body falls freely and accelerates at every point of its motion due to gravitational force alone. This is called acceleration of free fall.**Q.9. What do we call the gravitational force between the earth and an object? ****Ans.** Gravity is the name of the gravitational force between earth and the object.**Q.10. 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.] ****Ans.** Earth is not a perfect sphere. It is flattened at the poles. Thus, the value of ‘g’ is greater at poles than at equator (as g ∝ 1/r^{2}). This means weight of gold bought at poles becomes lesser at equator and the friend does not agree with the weight.**Q.11. ****Why will a sheet of paper fall slower than one that is crumpled into a ball?Ans.**

- Sheet crumpled into a ball has a small surface area as compared to that of an unfolded sheet. Therefore, the unfolded sheet will experience more friction due to air as compared to the crumpled ball in spite of the same force of gravity acting upon them.
- The larger friction of air slows down the unfolded sheet so it will fall slower than the sheet crumpled into a ball.

**Q.12. Gravitational force on the surface of the moon is only 1/6 as strong as gravitational force on the earth. What is the weight in newtons of a 10 kg object on the moon and on the earth? ****Ans.** Here, mass of object, m = 10 kg, g on the earth’s surface = 9.8 ms^{-2}

Weight of the object on the earth’s surface = mg

= 10 kg x 9.8 ms^{-2}

= 98.0 kg ms^{-2} = 98 N__The weight of object on moon is 1/6th that of object on earth, so the weight of the object on the moon:__= 1/6 x 98 N= 16.3 N.

(a) the maximum height to which it rises.

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

Maximum height, H = ?

Acceleration due to gravity, g = + 9.8 ms

As object is moving upward, so a = -g

From relation v

v

⇒ H = 122.5 m

∴ Relation, s = ut + at

0 = (49 ms

⇒ t (49 -4.9 t) = 0

t = 0 or 49 - 4.9 t = 0 ⇒ t =

As t ≠ 0, so t = 10s

The maximum height is 122.5 m and total time is 10 s.

Final velocity,

= 19.6 ms

► g = -10 ms

► Final velocity, v = 0

► During upward motion, g = -10 ms

► Net displacement on returning back = zero

► Total distance = 80 m + 80 m = 160 m

► Mass of sun M

► Distance, r = 1.5 x 10

► Gravitational constant, G = 6.67 x 10

► Force,

= 3.56 x 10

Let the stones meet at a height h above the ground. Stone 1 covers a distance (100 - h); g = 10 m/s

(100 - h) = 0 +

⇒ 100 - h = 5 t

► u

Stone 2 covers a distance h

g = - 10m/s

h = u

⇒ h = 25 t - 5 t

From (i) and (ii), we get

► 100 - 25 t + 5 t

► 100 - 25 t = 0

or t = 4 s (Stones meet 4 s after they are thrown)

h = 25(4) - 5(4)

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

(b) the maximum height it reaches.

(c) its position after 4s.

Ans.

Time of ascend = Time of descending

⇒ Time taken to reach the top, t = 3 s.

⇒ Final velocity, v = 0, g = -9.8 ms^{-2}.**(a)** Initial velocity, u = v - gt = 0 - (-9.8) (3)

= 29.4 ms^{-1}**(b) **Maximum height reached, h = (v^{2} - u^{2})/g = (29.4)^{2}/(2 x 9.8)

= 44.1 m**(c)** After 4s, ball has started falling and has fallen by some distance h' for 1s.

Here, initial velocity u' = 0, t = 1s

g = + 9.8 ms^{-1}

h' = u't + = 0 +

The ball is at a height, (44.1 - 4.9) = 39.2 m above the ground.**Q.19. In what direction does the buoyant force on an object immersed in a liquid act?****Ans.** An object immersed in a liquid experiences buoyant force in the upward direction.**Q.20. ****Why does a block of plastic released under water come up to the surface of water?Ans.**

- 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.

**Q.21. The volume of 50g of a substance is 20 cm ^{3}. If the density of water is 1g cm^{-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 =
- The density of the substance is more than the density of water (1 g cm
^{−3}). Hence, the substance will sink in water.

**Q.22. The volume of a 500 g sealed packet is 350 cm ^{3}. Will the packet float or sink in water if the density of water is 1 g cm^{-3}? What will be the mass of the water displaced by this packet? **

- Density of the 500 g sealed packet
- The density of the substance is more than the density of water (). 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 g.

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