ans: 1.26 × 10^(-6) N
mass of Justhin ( m) = 74 kg
mass of Christian (M) = 64 kg
distance of separation (d) = 0.5 m
universal gravitational constant(G) =6.67 × 10^(-11) Nm²/kg²
gravitational force between them(F) = GmM/d²
F = (6.67 × 74× 64)/ ( 10¹¹× 0.5²)
= (1.26 × 10⁵)/ 10¹¹
= 1.26 × 10^(-6) N
High amplitude is equivalent to loud sounds.
T₂ = 18.65 °C (For Steel)
The temperature of steel first becomes 12 MPa at a temperature of 18.65°C
The formula for stress due to temperature difference in a member is given as follows:
Stress = αEΔT
Stress = 12 MPa = 12 x 10⁶ Pa
α = co-efficient of linear expansion of the material
E = Young's Modulus of the Material
ΔT = Temperature Difference = Final Temperature - Initial Temperature
12 x 10⁶ Pa = αE(T₂ - 15°C)
α = 25.2 x 10⁻⁶ /°C
E = 45 x 10⁹ Pa
12 x 10⁶ Pa = (25.2 x 10⁻⁶/°C)(45 x 10⁹ Pa)(T₂ - 15°C)
T₂ - 15°C = (12 x 10⁶ Pa)/(1.134 x 10⁶ Pa/°C)
T₂ = 15°C + 10.58°C
T₂ = 25.58 °C (For Magnesium)
α = 17.3 x 10⁻⁶ /°C
E = 190 x 10⁹ Pa
12 x 10⁶ Pa = (17.3 x 10⁻⁶/°C)(190 x 10⁹ Pa)(T₂ - 15°C)
T₂ - 15°C = (12 x 10⁶ Pa)/(3.287 x 10⁶ Pa/°C)
T₂ = 15°C + 3.65°C
<u>T₂ = 18.65 °C (For Steel)</u>
<u>The temperature of steel first becomes 12 MPa at a temperature of 18.65°C</u>
The period of a pendulum is given by:
where L is the length of the pendulum and g is the free-fall acceleration on the planet.
In this problem, we know that the period of the pendulum on Earth is:
while the period of the same pendulum on Mars is
And since the length of the pendulum L does not change, we can write:
is the free-fall acceleration on Earth
is the free-fall acceleration on Mars
Re-arranging the equation and substituting numbers, we find:
The age of the universe can be calculated by : dark energy, the age of the oldest stars patterns of background radiation, and the speed of distant galaxies moving away from the Earth.
Anything that acts as a container for energy and matter is known as the universe. The modern definition of the universe is the place that has time itself including the other heavenly entities like Comets, meteors, Stars, Planets, and many more.
The age of the universe is determined by scientists using the following ways:
- Concept of dark energy is the property of space and it is used to predict the age of the universe as this form of energy is observed to expand the universe rapidly.
- The age of the oldest star patterns of background radiation is another way to determine the age of the universe as the first generation of stars are formed after the big bang.
- As per the Hubble's relation, the galaxies move away from the Earth at a certain speed are proportional to their distance. In other words, galaxies are farther as they are moving away from the Earth.
Thus, we can conclude that the age of the universe can be calculated by dark energy, the age of the oldest stars patterns of background radiation, and the speed of distant galaxies moving away from the Earth.
Learn more about the universe here: