can someone please help me to answer these questions?who answers it step by step of answer,, I will mark as brainliest.
1) Calculate the mass of Earth. Given, the force that Earth exerts on a mass (m) of 1 kg at its surface is 9.8 N. The radius of Earth ( R ) is
6. 4 × 106 m.
2) Calculate the force of gravity between two students with mass 55 kg and 45 kg and they are 1 m away from each other.
3) If a small asteroid named ‘B612’ has a radius of only 20 m and mass of 1 × 104 kg, what is the acceleration due to gravity on its surface?
4) If the gravitational force between objects of equal mass is2. 3 × 10−8 N, when the objects are 10 m apart, what is the mass of each object?
5) What is the gravitational force on a 70 kg object that is 6. 38 × 106 m
above the Earth’s surface?
Answers
Answer:
Question 1)
Given:
- Mass of object = 1 kg
- Force exerted = 9.8 N
- Radius of the Earth = 6.4 × 10⁶ m
- Mass of Earth = ?
According to Gravitational Force Formula,
Where, 'F' is the Gravitational Force, 'G' is the universal Gravitational constant, 'M' is the mass of larger body, 'm' is mass of smaller body & 'd' is the distance between the two bodies.
Substituting the given information, we get:
Hence the mass of the earth is 6.0181 × 10²⁴ Kg.
Question 2)
Given:
- Mass of Student 1 = 55 kg
- Mass of Student 2 = 45 kg
- Distance between them = 1 m
- Force of Gravity = ?
Using the Gravitational Force formula, we get:
Hence the force of gravity exerted between them is 1.6508 × 10⁻⁷ N.
Question 3)
Given:
- Radius of the asteroid = 20 m
- Mass of the asteroid = 1 × 10⁴ Kg
- Acceleration due to gravity = ?
The formula for calculating the acceleration due to gravity is given as:
Where, 'g' refers to the acceleration due to gravity, 'G' is the universal Gravitation Constant, 'M' refers to the mass of the object, 'd' refers to the distance from the center to it's surface.
Substituting the given information we get:
Hence the acceleration due to gravity on the asteroid's surface is 1.66 × 10⁻⁹ m/s².
Question 4)
Given:
- Force between 2 equal masses = 2.3 × 10⁻⁸ N
- Distance between the 2 objects = 10 m
- Mass of the object = ?
Using the gravitational force formula, we get:
Hence the mass of the object is 184.3 kg.
Question 5)
Given:
- Mass of the Earth = 6 × 10²⁴ kg
- Mass of the object = 70 kg
- Distance = 6.38 × 10⁶ m
- Gravitational Force = ?
Using the Gravitational Force formula we get:
Hence the gravitational force on the 70 kg object is 11.47 × 10⁻²³ N.
Answer:
Answer:
Question 1)
Given:
Mass of object = 1 kg
Force exerted = 9.8 N
Radius of the Earth = 6.4 × 10⁶ m
Mass of Earth = ?
According to Gravitational Force Formula,
\implies F_{G} = \dfrac{GMm}{d^2}⟹FG=d2GMm
Where, 'F' is the Gravitational Force, 'G' is the universal Gravitational constant, 'M' is the mass of larger body, 'm' is mass of smaller body & 'd' is the distance between the two bodies.
Substituting the given information, we get:
\begin{gathered}\implies 9.8\;N = \dfrac{6.67 \times 10^{-11} \times M_e \times 1}{(6.4 \times 10^6)^2}\\\\\\\implies M_e = \dfrac{9.8 \times 40.96 \times 10^{12}}{6.67 \times 10^{-11}}\\\\\\\implies M_e = 60.181 \times 10^{(12+11)}\\\\\\\implies \boxed{ M_e = 6.0181 \times 10^{24}\:\:Kg}\end{gathered}⟹9.8N=(6.4×106)26.67×10−11×Me×1⟹Me=6.67×10−119.8×40.96×1012⟹Me=60.181×10(12+11)⟹Me=6.0181×1024Kg
Hence the mass of the earth is 6.0181 × 10²⁴ Kg.
Question 2)
Given:
Mass of Student 1 = 55 kg
Mass of Student 2 = 45 kg
Distance between them = 1 m
Force of Gravity = ?
Using the Gravitational Force formula, we get:
\begin{gathered}\implies F_g = \dfrac{6.67 \times 10^{-11} \times 55 \times 45}{(1)^2}\\\\\\\implies F_g = 16508.25 \times 10^{-11} \:\:N\\\\\\\implies \boxed{F_g = 1.6508 \times 10^{-7} N}\end{gathered}⟹Fg=(1)26.67×10−11×55×45⟹Fg=16508.25×10−11N⟹Fg=1.6508×10−7N
Hence the force of gravity exerted between them is 1.6508 × 10⁻⁷ N.
Question 3)
Given:
Radius of the asteroid = 20 m
Mass of the asteroid = 1 × 10⁴ Kg
Acceleration due to gravity = ?
The formula for calculating the acceleration due to gravity is given as:
\implies g = \dfrac{GM}{d^2}⟹g=d2GM
Where, 'g' refers to the acceleration due to gravity, 'G' is the universal Gravitation Constant, 'M' refers to the mass of the object, 'd' refers to the distance from the center to it's surface.
Substituting the given information we get:
\begin{gathered}\implies g = \dfrac{6.67 \times 10^{-11} \times 1 \times 10^4}{(20)^2}\\\\\\\implies g = 0.0166 \times 10^{-7} \:\:m/s^2\\\\\\\implies \boxed{g = 1.66 \times 10^{-9}\:\:m/s^2}\end{gathered}⟹g=(20)26.67×10−11×1×104⟹g=0.0166×10−7m/s2⟹g=1.66×10−9m/s2
Hence the acceleration due to gravity on the asteroid's surface is 1.66 × 10⁻⁹ m/s².
Question 4)
Given:
Force between 2 equal masses = 2.3 × 10⁻⁸ N
Distance between the 2 objects = 10 m
Mass of the object = ?
Using the gravitational force formula, we get:
\begin{gathered}\implies 2.3 \times 10^{-8}\:\: N = \dfrac{6.67 \times 10^{-11} \times M^2}{(10)^2}\\\\\\\implies M^2 = \dfrac{2.3 \times 10^{-8} \times 10^2}{6.67 \times 10^{-11}}\\\\\\\implies M^2 = 0.34 \times 10^{(-8 + 2 + 11)}\\\\\\\implies M^2 = 3.4 \times 10^4\:\: kg^2\\\\\\\implies M = \sqrt{3.4 \times 10^4}\:\: kg\\\\\\\implies M = 1.843 \times 10^2\\\\\\\implies \boxed{M = 184.3\:\:kg}\end{gathered}⟹2.3×10−8N=(10)26.67×10−11×M2⟹M2=6.67×10−112.3×10−8×102⟹M2=0.34×10(−8+2+11)⟹M2=3.4×104kg2⟹M=3.4×104kg⟹M=1.843×102⟹M=184.3kg
Hence the mass of the object is 184.3 kg.
Question 5)
Given:
Mass of the Earth = 6 × 10²⁴ kg
Mass of the object = 70 kg
Distance = 6.38 × 10⁶ m
Gravitational Force = ?
Using the Gravitational Force formula we get: