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False

Explanation: G is also known as Universal Gravitational Constant. Value of G is 6.67×10⁻¹¹ Nm²kg^-2. The value of G is independent of mass of object and the distance between them.

The earth takes 365.25 days to complete one rotation around the sun. Hence it is uniform motion.

Weight of the scooter with rider = 150 kg 

Speed = 36 km/hr = 36 × \(\frac{5}{18}\) = 10 m/sec. 

Radius of the turning = 30 m 

The force needed on the scooter towards the centre is centripetal force.

Centripetal force F_c = \(\frac{mv^2}{r}=\frac{150\,\times\,10\,\times\,10}{30}\) = 500 N

∴ A centripetal force of 500 N is required on the car. 

This force is provided by the friction between the tyres of the car and road.

Height of Tower = 100 m

Time taken to reach ground = T seconds

Acceleration = a = g = 9.8 ms-2

Initial Speed = u = 0

Final Speed = v

Now, we know that,

S = ut + \(\frac{1}{2}\)at²

100 = \(\frac{1}{2}\)gT² At t = T and S = 100 m..........1

Let t = \(\frac{T}{2}\) and s = x

Then, x = \(\frac{1}{2}\)a\(\frac{T^2}{2}\)..........2

So, dividing equation 1 by 2, we get,

\(\frac{100}{\times}\) = 4

x = 25 m

So, 25 m from the top at t = \(\frac{T}{2}\) seconds or (100 - 25)m, that is 75 m from the bottom at \(\frac{T}{2}\)seconds.

Hence, option B is correct.

Now, initial separation = 1 m

Body 1:

Initial Speed = 0

Acceleration = 9.8 ms^-2

Time = 2 seconds

Now, we know that,

S = ut + \(\frac{1}{2}\)at²

So, S₁ = \(\frac{1}{2}\)x 9.8 x 4

S₁ = 19.6 m

Body 2:

Initial Speed = 0

Acceleration = 9.8 ms^-2

Time = 2 seconds

Now, we know that,

S = ut + \(\frac{1}{2}\)at²

^So, S₂ ⁼ \(\frac{1}{2}\)x 9.8 x 4

S₂ = 19.6 m

Since,S₁ = S₂ so final separation is also 1 m.

Hence, option D is correct.

False

Explanation: Force of attraction between two bodies is called gravitation.
Gravity is the force of attraction on any object by the earth that is a gravitational pull towards the centre of earth.

The force acting on these objects to make them move around another object, instead of moving in straight line in the gravitational force.

Centre of gravity of a human being is located interior to the second sacral vertebra. 

Centre of gravity of man lies out side the body in the following situation : 

a) While doing sit-ups. 

b) While carrying a load like bucket full of water with one hand.

c) While walking on a narrow base like walking on a rope or pole or narrow wall, etc. 

d) While walking with one leg. 

e) As age increases its position changes.

True

Explanation: Spring Balance gives the weight of the object.

W = m × g

If the heavy object is released, then it will read zero, since no mass implies no weight.

The earth’s atmosphere is about 10,000 km thick, but most of its bulk is contained in the first 11 km above the earth’s surface. Since the earth and its atmosphere are roughly spherical, the centre of the earth is also the centre of gravity of the earth’s atmosphere.

• The centre of gravity of a boy when he start erect, falls in the foot. 
• When he is doing sit-ups, the centre of gravity shifts from foot to his base.
• The weight vector also move from the base. 
• Hence the boy stretches his hands or bends slightly towards the earth. While doing sit ups, in order to make the weight vector pass through base, so that he acquire stability.

False

Explanation: G is universal gravitational constant and is always constant.
G = 6.67×10⁻¹¹ Nm²kg^-2

It does not change with radius of the body and thus is independent of it.

True

Explanation: Centre of mass means the mean position of all the matter in the body.

Centre of Gravity is a point at which the weight of body is considered.
If the object is small then gravitational field is uniform and both lie at the same point.

False

Explanation: Gravitational Force between two bodies does not change if a material body is placed between them, since according to Newton’s law,

F = G\(\frac{m_1\times m_2}{R^2}\)

Where, G = Universal gravitational Constant

m₁, m₂ = Masses of bodies

R = Distance between two bodies

Here, F does not depend on the material medium and hence it will not change due to change in medium.

It is so because the value of G is the same for all the pair of the bodies (big or small) situated anywhere in the universe.

The value of 'g' on the moon is small, therefore, the weight of moon-travellers will also be small.

The value of g on moon is small, therefore, the weight of moon travelers will also be small.

Relative density refers to the ratio of the density of a substance to the density of water. 

Relative Density = \(\frac{Density\,of\,a\,substance}{density\,of\,water}\)

(a) greater than 1: If the relative density is greater than 1, that means that the density of a substance is greater than the density of water. 

(b) less than 1: If the relative density is less than 1, that means that the density of a substance is less than the density of water. 

(c) equal to 1: If the relative density is equal to 1, that means that the density of a substance is equal to the density of water.

(a) The boat did not sink when Prateek used lighter dolls as the density of the dolls and the boat is much less than the density of water. 

(b) Buoyant Force is exerted by water on the objects immersed in it. The gravitational pull exerted on them is much more than the buoyant force therefore they sank. 

(c) Prateek is very patient as well as determined to achieve his goals. He does not lose hope and keeps on trying to fulfil what he wants.

Gravitational force depends on the mass of the object. The coin has more mass than the sheet of paper, therefore, force exerted on the coin will be more. On the other hand surface area of the sheet is more than coin; therefore air resistance will be more on the sheet of paper causing it to fall slow.

Archimedes’ principle states that when an object is fully or partially immersed in a fluid, it experiences an upward force that is equal to the weight of the fluid displaced by it. 

The two applications of Archimedes principle are: 

i) It is used to design ships and submarines. 

ii) It is used to design hydrometer which is used to measure the density of different liquids.

Mass of wooden block = 5 kg

Dimension of the block = 40 cm × 20 cm × 10 cm= 0.4 m × 0.2 m × 0.1 m 

Force = mass × acceleration due to gravity= 5 kg × 9.8 m/s² 

= 49 N 

(a) 20 cm × 10 cm 

Area = 20 cm × 10 cm = 0.2 m × 0.1 m = 0.02 m² 

Pressure =\(\frac{Force}{Area}\) = \(\frac{49}{0.02}\) = 2450 N/m² 

(b) 40 cm × 20 cm 

Area = 40 cm × 20 cm = 0.4 m × 0.2 m = 0.08 m² 

Pressure =\(\frac{Force}{Area}\) = \(\frac{49}{0.08}\) = 612.5 N/m².

Relative density of silver = 10.8 

The density of water = 10³ kg-m^–3 

Relative Density =\(\frac{Density\,of\,a\,substance}{density\,of\,water}\) = \(\frac{Density\,of\,silver}{density\,of\,water}\)

10.8 x 10³ kgm^–3 = Density of silver 

The density of silver = 10800 kg-m^–3

As the magnitude of buoyant force depends on the density of the liquid therefore if volume increases it will decrease the density and hence there will be no effect on the magnitude of buoyant force as it depends both on density and volume proportionally.

B = ρ_fvg

B- buoyant force in N

ρ_{f -} fluid density in kg/m³

V - displaced body volume of liquid in kg/m³

g = 9.806 m/s² ( standard gravity)

Early astronomers proved that Earth is spherical in shape by looking at the shape of the shadow cast by Earth on the Moon during lunar eclipse.

Gravitational force plays an important role for initiating the birth of stars, for controlling the entire structure of the universe and evolution of the universe. It helped to explain many natural phenomena.