<span>From the point of view of the astronaut, he travels between planets with a speed of 0.6c. His distance between the planets is less than the other bodies around him and so by applying Lorentz factor, we have 2*</span>√1-0.6² = 1.6 light hours. On the other hand, from the point of view of the other bodies, time for them is slower. For the bodies, they have to wait for about 1/0.6 = 1.67 light hours while for him it is 1/(0.8) = 1.25 light hours. The remaining distance for the astronaut would be 1.67 - 1.25 = 0.42 light hours. And then, light travels in all frames and so the astronaut will see that the flash from the second planet after 0.42 light hours and from the 1.25 light hours is, 1.25 - 0.42 = 0.83 light hours or 49.8 minutes.
Answer:
b. 3 times
Explanation:
Lets take
Coefficient for ordinary glass = α₁
Coefficient for pyrex glass = α₂
Given that α₁ = 3 α₂
Initial length of both glasses are equal = L
Change in the temperature is also same .= ΔT
We know that change in the length given as
ΔL = L α ΔT
Therefore


ΔL₁ = 3ΔL₂
Therefore change in the length of original glass is three time of pyrex glass.
b. 3 times
Explanation:
It is given that,
Density of asteroid, 
Mass of asteroid, 
We need to find the diameter of the asteroid. The formula of density is given by:

V is the volume of spherical shaped asteroid, 



r = 2441311.12 m
Diameter = 2 × radius
d = 4882622.24 m
or

Hence, this is the required solution.
Answer:
w = 0.943 rad / s
Explanation:
For this problem we can use the law of conservation of angular momentum
Starting point. With the mouse in the center
L₀ = I w₀
Where The moment of inertia (I) of a rod that rotates at one end is
I = 1/3 M L²
Final point. When the mouse is at the end of the rod
= I w + m L² w
As the system is formed by the rod and the mouse, the forces during the movement are internal, therefore the angular momentum is conserved
L₀ = L_{f}
I w₀ = (I + m L²) w
w = I / I + m L²) w₀
We substitute the moment of inertia
w = 1/3 M L² / (1/3 M + m) L² w₀
w = 1 / 3M / (M / 3 + m) w₀
We substitute the values
w = 1/3 / (1/3 + 0.02) w₀
w = 0.943 w₀
To finish the calculation the initial angular velocity value is needed, if we assume that this value is w₀ = 1 rad / s
w = 0.943 rad / s