**Unit : 7 Force And Motion**

**1. Choose the correct option for the following questions: **

**a). What happens to the gravitational force between two objects when their masses are both doubled?**

(i) The force doubles

(ii) the force becomes four-time

(iii) the force is reduced two times

(iv) The force is decreased four times **Answer (ii) the force becomes four-time Activate**

**b).** **If the gravitational force between two objects on Earth is 60 N, what would be the gravitational force between those two objects on the Moon?** (i) 10N

(ii) 6N

(iii) 9.8 N

(iv) 60 N **Answer (ii) 6N**

**d). Which one of the following statements is correct?**

(i) The value of acceleration due to gravity increases as we go deeper from the surface of the earth.

(ii) The value of acceleration due to gravity decreases as the height above the surface of the earth increases.

(iii) The value of acceleration due to gravity is less in the – polar region than that in the equatorial region.

(iv) The value of the acceleration of gravity is highest at the highest place on the Earth. **Answer: (ii) The value of acceleration due to gravity decreases as the height above the surface of the earth increases.**

**e). At which of the following places do you weight the most?**

(i) peak of Mount Everest

(ii) peak of Api Himal

(iii) Kechnakwal of JThapa

(iv) Chandragiri Hills**Answer: (i) peak of Mount Everest**

**f).Given that the radius of the Earth is 6371 km and the weight of an object on Earth’s surface is 800 N, what would be the weight of the object at a height of 6371 km from the surface of the Earth?**(i) 800N

(ii) 1600 N

(iii) 200 N

(iv) 3200 N

**Answer: (iii) 200 N**

**g). If a celestial body has a mass and radius that are both two times the mass and radius of Earth, what is the value of the acceleration due to gravity on that celestial body?**(i) 9.8 ms™

(ii) 4.9 ms™

(iii) 19.6ms™

(iv) 10ms TM

**Answer: (iii) 19.6ms™**

**h). What would be the weight of a person on the Moon if their weight on Earth is 750 N, considering the acceleration due to gravity on the Moon is approximately 1.63 m/s²?**(i) 124.74N

(ii) 125 N

(iii) 126.8 N

(iv) 127.8 N

**Answer: (ii) 125 N**

**2. Difference Between:**

**(a) Gravitational constant G and Acceleration due to gravity g**

Gravitational constant G | Acceleration due to gravity g: |

G is a constant number that never changes. | g represents the force of gravity experienced by an object due to a celestial body (like Earth or the Moon). |

It’s a universal value and is the same everywhere in the universe. | It varies depending on the celestial body and its mass. |

. Its value is approximately 6.674 × 10^{-11} N(m/kg)^{2}. | On Earth, g is approximately 9.81 m/s², which means objects near the Earth’s surface experience this acceleration. |

**(b) Mass and Weight**

Mass | Weight |

Mass is the amount of matter an object contains. | Weight is the force of gravity acting on an object’s mass. |

Mass is usually measured in kilograms (kg) or grams (g). | It depends on the gravitational pull of the celestial body you’re on (e.g., Earth, Moon, or Mars). |

It doesn’t change regardless of where you are in the universe; it’s an intrinsic property of the object. | It can vary depending on your location in the universe. |

**3. Give reason:**

**(a) Acceleration due to gravity is not the same in all parts of the earth.Ans:** Acceleration due to gravity is not the same in all parts of the earth because the Earth is not a perfect sphere, and its mass is distributed unevenly.

**(b) Jumping from a significant height may cause more injury.Ans:** When you jump from a high place, you have a lot of “falling” energy. When you hit the ground, all that energy needs to go somewhere, and it goes into your body. This can lead to more severe injuries like broken bones, because the higher you fall from, the more energy your body has to absorb when it stops suddenly on impact with the ground. So, jumping from a great height is riskier and can result in more harm to your body.

**(c) Mass of Jupiter is about 319 times the mass of the Earth, but its acceleration due to gravity is only about 2.6 times the acceleration due to gravity of the Earth.Ans:** Even though Jupiter has more mass, the fact that it’s so much bigger means you’re not pulled as strongly toward its center, which is why its gravity is only about 2.6 times that of Earth’s.

**(d) Among the objects dropped from the same height in the polar region and the equatorial region of the earth, the object dropped in the polar region falls faster.Ans:** In simple terms, objects fall faster in the polar region compared to the equatorial region because the Earth is spinning. At the equator, the Earth’s surface is moving faster due to this spin, and when you drop something there, it sort of inherits that eastward speed. This extra sideways motion makes the object take a bit longer to hit the ground. But in the polar region, where the Earth’s spin doesn’t affect objects as much, they fall to the ground faster because they don’t have that extra sideways push.

**(e) Out of two paper sheets, one is folded to form a ball. If the paper ball and the sheet of paper are dropped simultaneously in the air, the folded paper will fall faster.Ans:** The flat sheet has a larger surface area exposed to the air, so it experiences more air resistance, which slows it down. On the other hand, the ball has a smaller surface area in contact with the air, so it experiences less air resistance and falls faster

**(f) When a marble and a feather are dropped simultaneously in a vacuum, they reach the ground together (at the same time).Ans:** In a vacuum, there’s no air, so there’s no air resistance to slow things down. This means that all objects, no matter how heavy or light, fall at the same rate. So, the marble and feather fall together because nothing is holding them back in a vacuum, and gravity pulls them down at the same speed.

**(g) As you climb Mount Everest, the weight of the goods that you carry decreases.Ans:**As you climb Mount Everest, the weight of the goods that you carry decreases because the acceleration due to gravity decreases with increasing distance from the center of the Earth. The decrease in gravitational force results in a decrease in the effective weight of the objects being carried.

**(h) It is difficult to lift a big stone on the surface of the earth, but it is easy to lift a smaller one.Ans:** Big stones are harder to lift because they have more mass and a stronger pull from gravity, while smaller stones are easier to lift because they have less mass and a weaker pull from gravity..

**(i) Mass of an object remains constant but its weight varies from place to place.Ans:**Mass of the object remains constant because mass is the amount of matter contain in the object but weight is the force of gravity acting on an object’s mass. in simple term mass remains constant because it never changes no matter where you go in the universe but weight depend upon the gravity so, as gravity change place to place weight also change place to place.

**(j) One will have an eerie feeling when he/she moves down while playing a Rote Ping.Ans:** As you move downward on the Rote Ping, your body is pulled in the opposite direction of what you’re used to. Normally, gravity pulls you down towards the ground, so going against that feeling can be strange. It’s like your body is trying to float upward when you’re moving down, and that unusual sensation can make you feel eerie or weird. It’s a bit like the feeling you get when an elevator suddenly drops a short distance – your body isn’t expecting it, and it can give you an eerie feeling in your stomach.

**4. Answer the following questions:**

**(a) What is gravity?Ans:** Gravity is the invisible force that pulls things toward each other. It’s what makes objects fall when you drop them and keeps everything on Earth from floating away into space.

**(b) State Newton’s universal law of gravitation.Ans:** “Every object in the universe attracts every other object with a force. This force depends on two things: how much mass the objects have and how close they are to each other. The more massive the objects and the closer they are, the stronger the gravitational pull between them.” Mathematically, it can be represented as F = G x (m1 x m2) / r

^{2}, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers of mass.

**(c) Write the nature of gravitational force.Ans:** The nature of gravitational force explained in points:

i).Gravitational force is a natural force of attraction.

ii).It happens between any two objects with mass.

iii).The strength of this force depends on two things: the mass of the objects and how close they are.

iv).Bigger objects and closer objects have a stronger gravitational pull.

**(d) Define gravitational constant (G).Ans:** Gravitational constant (G) is a fundamental constant in physicsis It like a special number in science. It tells us how strong the force of gravity is between any two objects with mass. Its approximate value is 6.674 × 10

^{-11}N(m/kg)

^{2}.

**(e) Under what conditions is the value of gravitational force equal to the gravitational constant (F=G)?Ans:** The value of the gravitational force is equal to the gravitational constant (F = G) under the following conditions:

1).When you’re calculating the gravitational force between two objects with mass

2).When you use the formula F = G * (m1 * m2) / r

^{2}, where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.

**(f) Write two effects of gravitational force.Ans:** Two effects of gravitational force are:

**Falling Objects**: Gravity makes objects fall toward the Earth’s surface. When you drop something, like a ball, gravity pulls it down. This effect of gravity is why things don’t float away into space, and it’s also why you stay on the ground.

**Planetary Orbits**: Gravity keeps planets, like Earth, in orbit around the sun. The sun’s gravity pulls on the planets, and this tug-of-war between the planet’s motion and the sun’s gravity keeps them moving in a curved path. This is what causes the planets to go around the sun in their orbits.

**(g)Mathematically present the difference in the gravitation force between two objects when the mass of each is made double and the distance between them is made one forth their initial distance.Ans:**Mathematically, the difference in the gravitational force (F) between two objects when their masses are doubled (2m) and the distance between them is made one-fourth (r/4) of their initial distance (r) can be represented as follows:

Initial gravitational force: F1 = G x (mx m) /r

^{2}

New gravitational force: F2 = G x ((2m) x (2m)) / (r/4)

^{2}

Simplifying the equation:

F2 = G x (4m

^{2}) / (r

^{2}/16)

F2 = 16 x (G x m

^{2}) / (r

^{2})

F2 = 16 x F1

**Therefore, the new gravitational force (F2) is 16 times greater than the initial gravitational force (F1).**

**(h) What is gravitational force?Ans:** Gravitational force is the invisible pull that exists between objects with mass. It’s what makes things fall to the ground when you drop them and keeps planets in their orbits around the sun.

**(i) Define acceleration due to gravity.Ans:** Acceleration due to gravity is the acceleration experienced by an object when it is subjected to the gravitational force. It is the rate at which the velocity of an object changes under the influence of gravity. On the surface of the Earth, the average acceleration due to gravity is approximately 9.8 m/s².

**(i) What is free fall? Give two examples of it.Ans:** Free fall is when an object is falling under the influence of gravity alone, without any other forces acting on it, like air resistance or a propulsion system pushing it.Here are two examples of free fall:

**1).Dropping a Pen:**When you drop a pen from your hand, it goes into free fall. Gravity pulls it downward, and it accelerates until it hits the ground because there’s no other force stopping it.

**2).Skydiving:**When a person jumps out of an airplane with a parachute, they experience free fall during the initial part of the descent. At this stage, gravity is the only force acting on them until they open the parachute, which creates air resistance to slow them down.

**(k) Under what conditions is an object said to be in free fall?Ans:** An object is said to be in free fall when it is only influenced by gravity and no other forces, such as air resistance or external forces, are acting upon it. In free fall, the object experiences acceleration due to gravity and follows a parabolic trajectory.

**(l) Write the conclusions of the feather and coin experiment.Ans:** The conclusions of the feather and coin experiment are:

**i).**In the absence of air resistance (in a vacuum), objects with different masses, like a feather and a coin, fall at the same rate.

**ii).**Gravity affects all objects equally regardless of their mass when there is no air resistance. This means that in a vacuum, a heavy coin and a light feather will hit the ground at the same time if dropped from the same height.

**(m) What is weightlessness?Ans:** Weightlessness is a feeling like you’re floating, as if there’s no gravity pulling you down. It happens when you’re in a place, like in space during a spaceship orbit or freefall, where you and everything around you are falling together. Since everything falls at the same rate, it feels like there’s no force pushing you to the ground, making you feel weightless.

**(p) Mention the factors that influence acceleration due to gravity.Ans:** Acceleration due to gravity depends on two main factors:

**1).Mass of the Object:**The more massive an object is, the stronger its gravitational pull. So, if an object has more mass, it will have a higher acceleration due to gravity.

**2).Distance from the Center:**The closer you are to the center of a massive object, like the Earth, the stronger the gravitational pull. As you move away from the center, gravity gets weaker, and so does the acceleration due to gravity.

**(q) The acceleration due to the gravity in the Earth surface is 9.8 m/s2. What does this mean?Ans:** An acceleration due to gravity of 9.8 m/s² means that if you drop something from a height on Earth, it will speed up by 9.8 meters per second every second it falls. In simpler terms, it’s the rate at which objects on Earth get faster when they fall due to gravity. So, if you drop a ball, its speed increases by 9.8 meters per second for every second it’s in the air.

**(r) Mass of the Moon is about 1/81 times the mass of the Earth and its radius is about 37/10 times the radius of the Earth. If the earth is squeezed to the size of the moon, what will be the effect on its acceleration due to gravity? Explain with the help of mathematical calculation.**

To find out how the Earth’s acceleration due to gravity would change if it were squeezed to the size of the Moon, we can use the formula for gravitational acceleration:

$g=\frac{GM}{{R}^{2}}$

g is the gravitational acceleration

G is the gravitational constant (which is the same for both the Earth and the Moon)

M is the mass of the celestial body (Earth or Moon)

R is the radius of the celestial body (Earth or Moon)

Let’s consider the Earth first:

Mass of Earth(${M}_{E}$) is about 1 (because we are comparing it to itself).

Radius of Earth (${R}_{E}$) is the current radius of the Earth.

Now, let’s consider the Moon:

Mass of Moon(${M}_{M}$)is about $\frac{1}{81}$ times the mass of Earth.

Radius of Moon (${R}_{M}$) is about $\frac{37}{10}$ times the radius of Earth.

Now, let’s calculate the ratio of Earth’s acceleration due to gravity (${g}_{e}$) to Moon’s acceleration due to gravity(${g}_{m}$).

$\frac{{g}_{e}}{{g}_{m}}=\frac{\frac{G.{M}_{E}}{({R}_{E}{)}^{2}}}{\frac{G.{M}_{M}}{({R}_{M}{)}^{2}}}$

Now, plug in the values:

$\frac{{g}_{e}}{{g}_{m}}=\frac{\frac{1}{1}}{\frac{1}{\frac{1}{81}.(\frac{37}{10}{)}^{2}}}$

Now, calculate the value of $\frac{{g}_{e}}{{g}_{m}}$:

$\frac{{g}_{e}}{{g}_{m}}=\frac{1}{\frac{1}{\frac{1}{81}.\frac{1369}{100}}}$

Now, take the reciprocal of the fraction in the denominator:

$\frac{{g}_{e}}{{g}_{m}}=\frac{1}{\frac{100}{81}.\frac{100}{1369}}$

Now, calculate the value:

$\frac{{g}_{e}}{{g}_{m}}=\frac{1}{\frac{10000}{110889}}$

To simplify further, take the reciprocal of the fraction in the denominator:

$\frac{{g}_{e}}{{g}_{m}}=\frac{1}{\frac{110889}{10000}}$

Now, calculate the value:

$\frac{{g}_{e}}{{g}_{m}}=\frac{1}{11.0889}$

So, if the Earth were squeezed to the size of the Moon, its acceleration due to gravity would be approximately 11.0889 times stronger than the Moon’s gravity.

**(s) The acceleration due to gravity of an object of mass 1 kg in outer space is 2m/s?. What is the acceleration due to the gravity of another object of mass 10 kg at the same point? Justify with arguments.Ans:** The acceleration due to gravity is the same for objects of different masses at the same point. In this case, the acceleration due to gravity would be 2 m/s² for both the 1 kg object and the 10 kg object because it is determined by the gravitational field at that specific location in space, and the mass of the object experiencing the gravity does not change this value.

**(t) A man first measures the mass and weight of an object in the mountain and then in the Terai. Compare the data that he obtains.Ans:** When measuring the mass and weight of an object in the mountain and Terai regions, the mass of the object will remain the same in both places because mass is an intrinsic property of the object and doesn’t change with location.

**(u) A student suggests a trick for gaining profit in a business. He suggests buying oranges from the mountain selling them to Terai at the cost price.If a beam balance is used during this transaction, explain, based on scientific fact, whether his trick goes wrong or right.Ans**: The student’s trick to buy oranges from the mountain and sell them in Terai at the cost price could go wrong when using a beam balance. This is because the weight measured on the beam balance would indeed be different in the mountain and Terai due to the variation in the acceleration due to gravity. As a result, the trick would not result in equal profit since the weight of the oranges, and therefore their value, would vary depending on the location where they are weighed and sold.

**(v) How is it possible to have a safe landing while jumping from a flying airplane using a parachute? Is it possible to have a safe landing on the moon in the same way?Explain with reasons.****Ans:**. Using a parachute for a safe landing while jumping from a flying airplane is possible because the parachute increases air resistance, which counteracts the force of gravity. This gradual slowdown allows for a gentle landing.

**(w) The acceleration of an object moving on the earth is in-versely proportional to the mass of the object, but for an object falling towards the surface of the earth, the accel- eration does not depend on the mass of the object, why?Ans:**When an object is moving on Earth, the acceleration it experiences is inversely proportional to its mass, meaning lighter objects accelerate more for a given force. However, when an object is in free fall towards the surface of the Earth, the acceleration doesn’t depend on its mass. This is because gravity affects all objects equally during free fall, causing them to accelerate at the same rate, regardless of their mass. In this scenario, the mass doesn’t factor into the equation, resulting in the same acceleration for all objects.