Motion Under Gravity – Old Year Questions

• Brahmagupta, an eminent mathematician and astronomer of the 7th century, hailed from Bhinmal in Rajasthan.
• His renowned work, the ‘Brahmasphuta Siddhanta,’ is notable for his proclamation that all objects are attracted to the Earth through gravitational forces.

• In 1687, Isaac Newton wrote a book called “Mathematical Principles of Natural Philosophy”.
• In it, Newton said that every object in the universe is pulled towards each other, and the strength of this pull depends on the mass of the objects and how far apart they are.
• In math, this is called Newton’s law of gravity, and it says that the force between two objects (with masses m1 and m2) is equal to the product of their masses divided by the distance between them, squared.

F=G m₁m₂/r²
where, r = the distance between both the masses,
G = Gravitational constant.

• Isaac Newton said that all things in the universe pull on each other with a force.
• This force gets bigger when the masses of the objects are bigger and gets smaller when the distance between them is bigger.

• In space, astronauts can’t stand up because there is no gravity or microgravity which makes them feel like they are weightless.
• The lack of gravity affects the human body in different ways, like making muscles and bones weaker.

• If you let an apple go while inside a spaceship that is orbiting in space, it will stay with the spaceship and move at the same speed.

• The tower will stay upright as long as the weight of the tower is in the middle and within its base.
• This point in the middle is called the center of gravity.
• So far, the centre of gravity has been within the base, and that is why it has not fallen over.
• If it leans too far and the weight moves away from the base, it will collapse.

• The gravitational force that the Sun puts on Earth is determined by the distance between them, which we will call ‘r’. This is based on Newton’s Law of Universal Gravitation.

F₁= G M_sM_e/r²      ………………(1)
M_s= Mass of Sun
M_e= Mass of Earth
G = Gravitational constant
If the distance between the Earth and the sun were twice, then,
F2= G M_sM_e/(2r)² = G M_sMe/4r²    …………………. (2)
from equation (1) and (2)
F₁/F₂ = 4/1 ⇒ 4F₂ = F₁ ⇒ F2= 1/4 F₁

• Acceleration of the body is g downward.
  So a pseudo force will act in an upward direction which cancels the weight of the body.
  Hence the weight of the body in free fall is zero.

• When air resistance is not a factor, all objects of the same size, such as wood, wax, and iron, will reach the ground at the same time when dropped from the same height, regardless of their weight difference.
• This is because the same gravitational acceleration (g) affects all objects.

• If there is no air, the two balls will reach the ground at the same time.
• But with air, the iron ball will fall faster because it is smaller.
• The wood ball will take longer to fall because it is bigger and the air will slow it down.
• Therefore, option (c) is the correct answer.

• A and B will both hit the ground at the same time because they were both thrown from the same height of 20 meters.
• Thus, h = 20m
  Initial velocity u = 0
  speed equation (for gravitational velocity)
  V²= u²+ 2gh [ V → final velocity ]
  here, V²= 2gh ( u = 0)
  or V = √2gh
• Since the height of both balls are equal (h = 20) and the
  formula of final velocity (V = √2gh ) is not dependent on the
  mass of the balls. Thus, both the balls will reach the ground
  at the same time.

• The Moon is the only thing that orbits the Earth.
• The gravity on the Moon’s surface is only a sixth of the gravity on Earth, which means that a human’s weight on the Moon would be a sixth of their weight on Earth.
• This statement is true, but the reason why is not.

• The amount of gravity at a certain spot on the earth’s surface is always the same, but it is not the same everywhere.
• This is because the earth is not a perfect sphere; it is flatter at the poles and wider at the equator.
• The polar radius Rp is less than the equatorial radius Re. Now,
  g=Gm/r²
  Now, as ‘G’ & ‘M’ remain constant, therefore
  g α 1/R²
• Thus the value of ‘g’ is minimum at the equator and maximum at the poles.
• It means ‘g’ increases as we move from the equator to the poles.

• R Gravity’s acceleration is the same at one spot, but differs from place to place on the Earth.
• This is because the Earth isn’t a perfect sphere; it’s flatter at the poles and wider at the equator.
• The polar radius is shorter than the equatorial radius.
• g=Gm/r²
  Now, as ‘G’ & ‘M’ remain constant, therefore
  g α 1/R²
• Thus the value of ‘g’ is minimum at the equator and maximum at the poles.
• It means ‘g’ increases as we move from the equator to the poles.

• According to the question,
  a = 9.8 m/s², t= 3 sec., u = 0
  we know that, v = u + at = 0 + 9.8 × 3 = 29.4 m/s.

• We know that g = GM/r²      ……………….(i)
  After shrinking by 1% new radius will be 0.99 R
  Then, g’ = GM/(0.99R)²      ………………..(ii)
  g’/g  = R²/(0.99R)² = 1/(0.99R)² = 1.02
  From equation (i) and (ii)
  ⇒ g’ = 1.02g
  Thus, the value of g is increased by 2%

• The acceleration due to the gravity of a catastrophic earthquake
  will be greater than 980 cm/sec²or 9.8 m/sec².

• The amount of matter in a body stays the same no matter the gravity.
• The amount of force it feels due to gravity is different depending on if it’s on Earth or the moon, but the body’s mass remains the same.

• Weightlessness happens when there is nothing to hold you up.
• If you are falling at the same speed as gravity, you feel like you have no weight. People usually refer to this as “zero gravity”.
• You usually feel the weight because something is supporting you, like the ground or a chair.

• The Earth rotates and travels around the sun in its orbit. We don’t sense this motion since we are travelling with the Earth. We move at the same speed as the Earth does.
• To observe the Earth’s motion, we can look at objects that are not connected to the Earth like the Sun or stars.
• An example would be when you are in a car that is driving on a flat surface, you don’t feel the motion, but when the car accelerates or brakes, you do feel the motion.

• If gravity on Earth stopped working, the weight of objects would be nothing but their mass would stay the same.

• A satellite that circles the Earth does not fall because the Earth’s gravity pulls it in a curved path, giving it the speed it needs to stay in orbit.

• Centripetal force is a real force that keeps an object moving in a circular or elliptical path at a constant speed, instead of allowing it to fly away.
• Gravity is the centripetal force that keeps planets orbiting around the sun and satellites orbiting around planets.

• A geosynchronous satellite is a satellite that follows an orbit around the Earth in which it takes 24 hours to complete one circle.
• This is made possible by the force of gravity, which is a force that pulls together objects that have mass.

• Gravity is the weakest of the four basic forces, while the strongest is the strong nuclear force.

• Let the mass of the person is ‘m’ and weight is ‘w’ and the
  elevator going upward with acceleration ‘a’. The force acting
  on person1. the force due to gravity = mg
  2. the force giving the acceleration = ma
  According to Newton’s second laww – mg = ma
  w = m (g + a)
• So, it is clear that when the elevator is going upward
  expeditiously a person actually feels a little heavier than his
  usual weight and on the other hand when elevator accelerates
  downward then a person feels a little reduction than his usual
  weight.

• The time period of a pendulum depends on its length. As we know that T = 2π √l/√g , thus the result is that the one variable that affects the period of the pendulum is the length of the string.
• Increases in the length lead to increases in the period.

• Time period of simple pendulum T = 2π √l/√g
  where l = length of the pendulum
• In the summertime, the pendulum in clocks is longer.
• This makes the clock tick slower, causing it to run slower than usual.

• A girl is swinging on a swing while sitting, but when she stands up, she moves her body higher, which makes the swing’s pendulum shorter.
• This makes the swing’s time shorter.

• When an object is in simple periodic motion and it passes through its mean position, it has no force acting on it, its acceleration is zero, it has maximum velocity and maximum kinetic energy, and it has zero potential energy.
• When the object reaches its extreme position, its acceleration is at its maximum, there is a counterforce acting on it, it has no kinetic energy, has maximum potential energy, and has zero velocity.
• Each time the object rotates, it has a specific velocity twice, but usually, the oscillation of the pendulum decreases with time due to air resistance, so statements 1, 2, and 4 are correct but statement 3 is wrong.

• A pendulum clock runs faster in winter because the pendulum’s swing gets shorter when it’s cold, causing the clock to speed up.

• The escape velocity is the lowest speed an object must have to get away from the gravitational pull of a planet, like Earth which is 11.2 km/sec.

• The escape velocity of the Earth is 11.2 km/sec, which is the lowest speed needed to break free from Earth’s gravity.
• Anything moving slower than this will come back to the Earth.

• The moon has no atmosphere because gravity on the moon is weak, causing the escape velocity to be weak too.
• The speed of gas molecules is much higher than the escape velocity, so they all escape and the moon is left without an atmosphere.

• NASA’s experiment showed that gravity is needed to light a candle.
• In a spacecraft, a flame can be lit, but not in a real vacuum.
• The frequency of the flame’s flickering is related to the acceleration of gravity and the size of the candle.
• Since there is no gravity in space, the flame won’t light, so the answer is (a).

• When in a state with no gravity, the flame of a candle will be round.