Question 1

Q1: How does the force of gravitation between two objects change when the distance between them is reduced to half ?

Accepted Answer

The force of gravitation is inversely proportional to the square of the distance between two objects. If the distance is reduced to half, the gravitational force becomes four times greater. If the initial distance is $d$, the force is $F = G\frac{Mm}{d^2}$. If the distance becomes $\frac{d}{2}$, the...

Question 2

Q10: 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 t...

Accepted Answer

The friend will not agree with the weight of the gold. Weight is given by $W = mg$, where $m$ is the mass and $g$ is the acceleration due to gravity. The mass of the gold remains the same, but the value of $g$ is greater at the poles than at the equator. Therefore, the weight of the gold will be les...

Question 3

Q11: Why will a sheet of paper fall slower than one that is crumpled into a ball?

Accepted Answer

A sheet of paper falls slower than a crumpled ball of paper due to air resistance. The sheet of paper has a larger surface area exposed to the air, resulting in greater air resistance opposing its motion. The crumpled ball has a smaller surface area, so it experiences less air resistance. In a vacuu...

Question 4

Q12: 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...

Accepted Answer

Given: Mass of the object, $m = 10 	ext{ kg}$ Acceleration due to gravity on Earth, $g_e = 9.8 	ext{ m/s}^2$ Acceleration due to gravity on Moon, $g_m = \frac{1}{6} g_e$ To Find: Weight on Earth, $W_e$, and Weight on Moon, $W_m$ Formula: $$W = mg$$ Calculation: Weight on Earth: $$W_e = m g_e = 10...

Question 5

Q13: A ball is thrown vertically upwards with a velocity of $49 	ext{ m/s}$. Calculate (i) the maximum height to which it rises, (ii) the total time it ta...

Accepted Answer

Given: Initial velocity, $u = 49 	ext{ m/s}$ Final velocity at maximum height, $v = 0 	ext{ m/s}$ Acceleration due to gravity, $g = -9.8 	ext{ m/s}^2$ (negative because it opposes the motion) (i) To Find: Maximum height, $h$ Formula: $$v^2 = u^2 + 2gh$$ Calculation: $$0 = (49)^2 + 2 	imes (-9.8)...

Question 6

Q14: A stone is released from the top of a tower of height 19.6 m . Calculate its final velocity just before touching the ground.

Accepted Answer

Given: Height of the tower, $h = 19.6 	ext{ m}$ Initial velocity, $u = 0 	ext{ m/s}$ Acceleration due to gravity, $g = 9.8 	ext{ m/s}^2$ To Find: Final velocity, $v$ Formula: $$v^2 = u^2 + 2gh$$ Calculation: $$v^2 = 0^2 + 2 	imes 9.8 	imes 19.6$$ $$v^2 = 2 	imes 9.8 	imes 19.6 = 384.16$$ $$v...

Question 7

Q15: A stone is thrown vertically upward with an initial velocity of $40 	ext{ m/s}$. Taking $g=10 	ext{ m/s}^{2}$, find the maximum height reached by th...

Accepted Answer

Given: Initial velocity, $u = 40 	ext{ m/s}$ Final velocity at maximum height, $v = 0 	ext{ m/s}$ Acceleration due to gravity, $g = -10 	ext{ m/s}^2$ (negative because it opposes the motion) To Find: Maximum height, $h$, net displacement, and total distance covered Formula: $$v^2 = u^2 + 2gh$$ Ca...

Question 8

Q16: Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth $=6 	imes 10^{24} 	ext{ kg}$ and of the Sun $=2 \...

Accepted Answer

Given: Mass of the Earth, $M_e = 6 	imes 10^{24} 	ext{ kg}$ Mass of the Sun, $M_s = 2 	imes 10^{30} 	ext{ kg}$ Distance between the Earth and the Sun, $d = 1.5 	imes 10^{11} 	ext{ m}$ Gravitational constant, $G = 6.67 	imes 10^{-11} 	ext{ N m}^2 	ext{ kg}^{-2}$ To Find: Gravitational force,...

Question 9

Q17: A stone is allowed to fall from the top of a tower 100 m high and at the same time another stone is projected vertically upwards from the ground with...

Accepted Answer

Given: Height of the tower, $h = 100 	ext{ m}$ Initial velocity of the first stone (falling from the top), $u_1 = 0 	ext{ m/s}$ Initial velocity of the second stone (projected upwards), $u_2 = 25 	ext{ m/s}$ Acceleration due to gravity, $g = 9.8 	ext{ m/s}^2$ To Find: Time $t$ and distance from...

Question 10

Q18: A ball thrown up vertically returns to the thrower after 6 s . Find (a) the velocity with which it was thrown up, (b) the maximum height it reaches, a...

Accepted Answer

Given: Total time of flight, $T = 6 	ext{ s}$ Acceleration due to gravity, $g = -9.8 	ext{ m/s}^2$ (a) Time to reach maximum height, $t = \frac{T}{2} = \frac{6}{2} = 3 	ext{ s}$ At maximum height, $v = 0 	ext{ m/s}$ To Find: Initial velocity, $u$ Formula: $$v = u + gt$$ Calculation: $$0 = u + (-...

Question 11

Q19: In what direction does the buoyant force on an object immersed in a liquid act?

Accepted Answer

The buoyant force on an object immersed in a liquid acts in the upward direction, opposite to the direction of gravity.

Question 12

Q2: Gravitational force acts on all objects in proportion to their masses. Why then, a heavy object does not fall faster than a light object?

Accepted Answer

The acceleration due to gravity is independent of the mass of the object. From the universal law of gravitation: $F = G\frac{Mm}{R^2}$, where $M$ is the mass of the Earth and $m$ is the mass of the object, and $R$ is the radius of the Earth.  The force acting on the object due to gravity is also giv...

Question 13

Q20: Why does a block of plastic released under water come up to the surface of water?

Accepted Answer

A block of plastic released under water comes up to the surface of water because the density of plastic is less than the density of water. The buoyant force (upward force) exerted by the water on the plastic block is greater than the weight of the plastic block (downward force due to gravity). There...

Question 14

Q21: The volume of 50 g of a substance is $20 	ext{ cm}^{3}$. If the density of water is $1 	ext{ g cm}^{-3}$, will the substance float or sink?

Accepted Answer

Given: Mass of the substance, $m = 50 	ext{ g}$ Volume of the substance, $V = 20 	ext{ cm}^3$ Density of water, $ho_w = 1 	ext{ g/cm}^3$ To Find: Whether the substance floats or sinks Formula: $$	ext{Density} = \frac{	ext{Mass}}{	ext{Volume}}$$ Calculation: Density of the substance: $$ho_s...

Question 15

Q22: The volume of a 500 g sealed packet is $350 	ext{ cm}^{3}$. Will the packet float or sink in water if the density of water is 1 g $	ext{cm}^{-3}$ ?...

Accepted Answer

Given: Mass of the packet, $m = 500 	ext{ g}$ Volume of the packet, $V = 350 	ext{ cm}^3$ Density of water, $ho_w = 1 	ext{ g/cm}^3$ To Find: Whether the packet floats or sinks, and the mass of the water displaced Formula: $$	ext{Density} = \frac{	ext{Mass}}{	ext{Volume}}$$ Calculation: Dens...

Question 16

Q3: What is the magnitude of the gravitational force between the earth and a 1 kg object on its surface? (Mass of the earth is $6 	imes 10^{24} 	ext{ kg...

Accepted Answer

Given: Mass of the Earth, $M = 6 	imes 10^{24} 	ext{ kg}$ Radius of the Earth, $R = 6.4 	imes 10^{6} 	ext{ m}$ Mass of the object, $m = 1 	ext{ kg}$ Gravitational constant, $G = 6.67 	imes 10^{-11} 	ext{ N m}^2 	ext{ kg}^{-2}$ To Find: Gravitational force $F$ Formula: $$F = G\frac{Mm}{R^2}$$...

Question 17

Q4: The 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...

Accepted Answer

The Earth and the Moon attract each other with the same force.  This is in accordance with Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.  The gravitational force between two objects is mutual and equal in magnitude, although opposite in di...

Question 18

Q5: If the moon attracts the earth, why does the earth not move towards the moon?

Accepted Answer

According to Newton's second law of motion, $F = ma$, or $a = \frac{F}{m}$. The acceleration is inversely proportional to the mass. The Earth does accelerate towards the Moon due to the Moon's gravitational attraction, but because the Earth's mass is much larger than the Moon's mass, the Earth's acc...

Question 19

Q6: 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?...

Accepted Answer

(i) If the mass of one object is doubled, the gravitational force between the objects is also doubled, because the force is directly proportional to the product of the masses. (ii) If the distance between the objects is doubled, the gravitational force becomes one-fourth of the original force, becau...

Question 20

Q7: What is the importance of universal law of gravitation?

Accepted Answer

The universal law of gravitation explains several phenomena: (i) It explains the force that binds us to the Earth. (ii) It explains the motion of the Moon around the Earth. (iii) It explains the motion of planets around the Sun. (iv) It explains the tides due to the Moon and the Sun.  Essentially, i...

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