Answer:
The time taken to rotate the sphere one time is, t = 22 s
Explanation:
Given data,
The mass of the sphere, m = 8200 kg
The radius of the sphere, r = 90 cm
= .9 m
The force applied by the girl, F = 75 N
The moment of inertia of the sphere is,
I = 2/5 mr²
= (2/5) 8200 x (.9)²
= 2657 kg·m²
The torque,
τ = I α
75 x 0.9 = 2657 x α
α = 0.0254 rad/s²
The angular displacement,
θ = ½αt²
2π = ½ x 0.0254 rad/s² x t²
t = 22 s
Hence, the time taken to rotate the sphere one time is, t = 22 s
<h2>
The average speed of the moon around the earth is 1021.74 m/s</h2>
Explanation:
Radius of moon around earth, r = 3.84 × 10⁸ m
Circumference of orbit = 2πr = 2 x 3.14 x 3.84 × 10⁸
Circumference of orbit = 2.41 x 10⁹ m
Time taken, t = 27.3 days = 27.3 x 24 x 60 x 60 = 2358720 seconds
We have
Circumference of orbit = Speed of moon x Time taken
2.41 x 10⁹ = Speed of moon x 2358720
Speed of moon = 1021.74 m/s
The average speed of the moon around the earth is 1021.74 m/s
Complete Question
You stand on a straight desert road at night and observe a vehicle approaching. This vehicle is equipped with two small headlights that are 0.681 m apart. At what distance, in kilometres, are you marginally able to discern that there are two headlights rather than a single light source?Take the wavelength of the light to be 549 nm and your pupil diameter as 4.63 mm.
Answer:
The distance is 
Explanation:
From the question we are told that
The is distance between the headlight is 
The wavelength is 
The pupil diameter is 
Generally, we can mathematically evaluate the resolution of the eye as

substituting values

Now according to SOHCAHTOA rule

Where z is the distance at which the eye can discern the two head light
given that the angle is very small 
=> 
substituting values

=> 
=> 