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Science Question Answer (3 Marks)

Gravitation · Maharashtra Board STD 9 (MSBSHSE - Semi English Medium). 20 questions.

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Question Answer (3 Marks)

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Question 13 Marks
A stone is thrown vertically upwards with a speed of $20 m / s$. How high will it go before it begins to fall?
$\left( g =9.8 m / s ^2\right)$
Answer
Initial velocity, $u =20 m / s$
Final velocity, $v=0$
Acceleration due to gravity, $g=-9.8 m / s ^2$
Height, $h =$ ?
Using relation, for a freely falling body:
$v^2=u^2+2 g h$
$(0)^2=(20)^2+2 \times(-9.8) \times h$
$0-400=-19.6 h$
$h=\frac{400}{19.6}=20.4 m$
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Question 23 Marks
A stone is dropped from a height of $20\ m$.
What will be its speed when it hits the ground? $(g = 10m/s^2)$
Answer
Height, $s = 20\ m$
Initial velocity, $u = 0$
Acceleration due to gravity, $g = 10m/s^2$
Final velocity, $v = ?$
Time taken, $t = ?$
For a freely body.
$\text{v}^2=\text{u}^2+2\text{gh}$
$=(0)^2+2\times(10)\times(20)$
So, $\text{v}^2=400$
$\text{v}=\sqrt{400}=20\text{m/s}$
The speed of stone when it hits the ground will be $20m/s$.
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Question 33 Marks
Explain why, when a person stands on a cushion, the depression is much more than when he lies down on it.
Answer
When a person stands on a cushion then only his two feet (having small area) are in contact with the cushion. Due to this the weight of man falls on a small area of the cushion producing a large pressure causing a big depression in the cushion. On the other hand, when the same person lies down on the cushion, then his whole body (having large area) is in contact with the cushion.
Here, his weight falls on a much larger area of the cushion producing much smaller pressure and very little depression in the cushion.
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Question 43 Marks
What is the difference between the density and relative density of a substance?
Answer
  • Density: The density of a substance is defined as mass of the substance per unit volume.
Density of substance $=\frac{\text{mass or substance}}{\text{volume of substance}}$

SI unit of density is $kg/m^3$.
  • Relative density: The relative density of a substance is the ratio of its density to that of water.
Relative Density of substance $=\frac{\text{Density of substance}}{\text{Density of water}}$

It has no unit
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Question 53 Marks
5kg of material A occupy $20\ cm^3$ whereas $20\ kg$ of material B occupy $90\ cm^3$​​​​​​​​​​​​​​. Which has the greater density: A or B? Support your answer with calculations.
Answer
For material A:
Mass $= 5\ kg$
Volume of $20\ cm$
$= 20 \times 10^{-6}m^3$
Density of material $\text{A}=\frac{5}{20\times10^{-6}}=0.25\times10^6\text{kg}/\text{m}^3$
For material B:
Mass $= 20\ kg$
Volume $= 90\ cm^3$
$= 90 \times 10^{-6}\ m^3$​​​​​​​
Density of material $\text{A}=\frac{20}{90\times10^{-6}}=0.22\times10^6\text{kg}/\text{m}^3$
Density of material A is more than density of material B.
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Question 63 Marks
A piece of stone is thrown vertically upwards. It reaches the maximum height in 3 seconds. If the acceleration of the stone be $9.8 m / s ^2$ directed towards the ground, calculate the initial velocity of the stone with which it is thrown upwards.
Answer
Initial velocity of the stone, $u =$ ?
Final velocity of stone, $v =0$
Acceleration due to gravity, $g=-9.8 m / s ^2$
Time, $t =3 \sec$
Using relation, $v = u + gt$
$0  =u-9.8 \times 3$
$u  =29.4 m / s$
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Question 73 Marks
State the universal law of gravitation. Name the scientist who gave this law.
Answer
According to universal law of gravitation: Every body in the universe attracts every other body with a force (F) which is directly proportional to the product of their masses (m and M) and inversely proportional to the square of the distance (d) between them.
$\text{F}=\text{G}\times\frac{\text{m}\times\text{M}}{\text{d}^2}$
Sir Isaac Newton gave this law.
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Question 83 Marks
Can we apply Newton’s third law to the gravitational force? Explain your answer.
Answer
Yes, Newton’s third law of motion holds good for the force of gravitation. This means that when earth exerts a force of attraction on an object, then the object also exerts an equal force on the earth, in the opposite direction.
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Question 93 Marks
A girl is wearing a pair of flat shoes. She weighs $550\ N$ . The area of contact of one shoe with the ground is $160 cm^2$. What pressure will be exerted by the girl on the ground:
a. If she stands on two feet?
b. If she stands on one foot?
Answer
Force, $F =550 N$
Area of contact of one shoe $=160 cm^2$
$=160 \times 10^{-4} m^2$
Area of contact with two shoes $=160 \times 2=320 cm^2$
$=320 \times 10^{-4} m^2$
a. If the girl stands on two feet,
Pressure $=\frac{\text { Force }}{\text { Ares }}$
$=\frac{550}{320 \times 10^{-4}}=17187.5 N / m^2$
b. If she stands on one foot,
$\text { Pressure }=\frac{\text { Force }}{\text { Area }}$
$=\frac{550}{160 \times 10^{-4}}=34375 N / m^2$
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Question 103 Marks
Why does a ship made of iron and steel float in water whereas a small piece of iron sinks in it?
Answer
A ship made of iron and steel is a hollow object which contains a lot of air in it. Due to the presence of a lot of air in it, the average density of the ship becomes less than the density of water. Hence a ship floats in water.
On the other hand, a piece of iron is denser than water, so it sinks in water.
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Question 113 Marks
When a cricket ball is thrown vertically upwards, it reaches a maximum height of $5$ meters.
  1. What was the initial speed of the ball?
  2. How much time is taken by the ball to reach the highest point? (g = $10ms^{-2}$^)
Answer
Initial velocity, $u = ?$
Final velocity, $v = 0$
Acceleration due to gravity, $g = -10m/s^2$
Height, $h = 5\ m$​​​​​​​
  1. For a freely falling body:
$v^2 = u^2 + 2gh$
$(0)^2 = u^2+ 2 \times (-10) \times 5$
$0 = u^2 -100$
$u^2 = 100$
So, $u = 10\ m/s$​​​​​​​
  1. Using relatio $n, v = u + gt$
$0 = 10 + (-10)t$
$-10 = -10t$
$t = 1\  sec$
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Question 123 Marks
Calculate the density of an object of volume $3m^3$ and mass $9\ kg$. State wheater this object will float or sink in water. Give reason for your answer.
Answer
Volume $= 3\ m^3$​​​​​​​
Mass $= 9\ kg$
Density of substance $=\frac{\text{Mass of substance}}{\text{Volume of substance}}$
Density of substance $=\frac{9}{3}=3\text{kg}/\text{m}^3$
And density of water $= 1000\ kg/m^3$​​​​​​​
The object will float in the water as the density of the object is less than the density of water.
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Question 133 Marks
When is the pressure on the ground more-when a man is walking or when a man is standing? Explain.
Answer
When a man is walking, then at one time only one foot is on the ground. Due to this, the force of weight of man falls on a smaller area of the ground and produces more pressure on the ground. On the other hand, when the man is standing, then both his feet are on the ground. Due to this, the weight of the man falls on a larger area of the ground and produces lesser pressure on the ground.
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Question 143 Marks
Calculate the acceleration due to gravity on the surface of a satellite having a mass of $7.4 \times 10^{22} kg$ and a radius of $1.74 \times 10^6 m\left( G =6.7 \times 10^{-11} Nm ^2 / kg ^2\right)$. Which satellite do you think it could be?
Answer
Acceleration due to gravity,
Mass, $M =7.4 \times 10^{22} kg$
Radius, $R=1.74 \times 10^6 m$
Gravitational constant, $G =6.7 \times 10^{-11} Nm ^2 / kg ^2$
$g =6.7 \times 10^{-11} \times \frac{7.4 \times 10^{22}}{\left(1.74 \times 10^8\right)^2}$
$g =\frac{6.7 \times 7.4}{1.74 \times 1.74 \times 10}$
$g =1.637 m / s ^2$
As the value of $g =1.637 m / s ^2$, which is one sixth the value of g on earth, the satellite could be moon.
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Question 153 Marks
If the relative density of a substance is 7.1, what will be its density in SI units?
Answer
Relative Density of substance $=\frac{\text{Density of substance}}{\text{Density of water}}$
$7.1=\frac{\text{Density of substance}}{1000\text{kg}/\text{m}^3}$
Density of substance $=7.1\times10^3\text{kg}/\text{m}^3$
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Question 163 Marks
The mass of sun is $2 \times 10^{30}\  kg$ and the mass of earth is $6 \times 10^{24}\ kg$. If the average distance between the sun and the earth be $1.5 \times 10^8\  km$, calculate the force of gravitation between them.
Answer
Distance $d =1.5 \times 10^8 km=1.5 \times 10^{11} m$
Mass of the sun, $m =2 \times 10^{30} kg$
Mass of the earth, $M=6 \times 10^{24} kg$
Force of gravitation, $F=G \times \frac{\operatorname{m} \times M }{ d ^2}$
$F=6.7 \times 10^{-11} \times \frac{2 \times 10^{30} \times 6 \times 10^{24}}{\left(1.5 \times 10^{11}\right)^2}$
$F=\frac{6.7 \times 10^{-11} \times 12 \times 10^{54}}{1.5 \times 1.5 \times 10^{22}}$
$F=\frac{6.7 \times 12 \times 10^{21}}{1.5 \times 1.5}=3.57 \times 10^{22} N$
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Question 173 Marks
Describe how the gravitational force between two objects depends on the distance between them.
Answer
The gravitational force F between two bodies of masses M and m kept at a distance d from each other is:
$\text{F}=\text{G}\times\frac{\text{m}\times\text{M}}{\text{d}^2}$
The force between two bodies is inversely proportional to the square of the distance between them. That is,
$\text{F}\propto\cfrac{1}{\text{d}^2}$
Therefore, if we double the distance between two bodies, the gravitational force becomes one-fourth and if we halve the distance between two bodies, then the gravitational force becomes four times.
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Question 183 Marks
A $\frac{1}{2}\text{kg}$ sheet of tin sinks in water but if the same sheet is converted into a box or boat, it floats. Why?
Answer
The sheet of tin sinks in water because the density of tin is higher than that of water. When the same sheet of tin is converted into a box or a boat, then due to the trapping of lot of ‘light’ air in the box or boat, the average density of the box or boat made of tin sheet becomes lower than that of water and hence it floats in water.
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Question 193 Marks
Define gravitational constant. What are the units of gravitational constant?
Answer
The gravitational constant $\text{G}$ is numerically equal to the force of gravitation which exists between two bodies of unit masses kept at a unit distance from each other.
$\text{G}=\text{F}\times\frac{\text{d}^2}{\text{m}\times\text{M}}$
units of gravitational constant $= NM^2/kg^2.$
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Question 203 Marks
Is the acceleration due to gravity of earth ‘g’ a constant? Discuss.
Answer
No, the value of acceleration due to gravity (g) is not constant at all the places on the surface of the earth. Since the radius of the earth is minimum at the poles and maximum at the equator, the value of g is maximum at the poles and minimum at the equator. As we go up from the surface of the earth, the distance from the centre of the earth increases and hence the value of g decreases. The value of g also decreases as we go down inside the earth.
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Question Answer (3 Marks) - Science STD 9 Questions - Vidyadip