Given Information:
Diameter = d = 100 m
Required Information:
Period = T = ?
Answer:
Period = T = 14.2 seconds
Explanation:
We know that a station revolving at an angular velocity ω, have an acceleration given by
α = ω²r
Where ω is angular velocity and r is the radius of cylindrical space station.
Normal gravity means α = g = 9.8 m/s²
ω² = α/r
ω = √(α/r)
The radius is given by
r = d/2
r = 100/2
r = 50 m
ω = √(9.8/50)
ω = 0.4427 rad/sec
We also know that
ω = 2πf
f = ω/2π
f = 0.4427/2π
f = 0.0704 rev/sec
Finally time period is given by
T = 1/f
T = 1/0.0704
T = 14.2 sec
Therefore, the rotation period is 14.2 seconds.
Answer:

Explanation:
L = Initial length of segment = 79 m
T = Normal temperature = 
l = Width to be left for expansion
= Coefficient of linear expansion of the material = 
= Maximum temperature = 
= Change in temperature = 
The expression of linear expansion is given by

The expression for the minimum gap distance l the engineers must leave for a track rated at temperature
is 
Answer:
138.18 minutes
Explanation:
= Latent heat of water at 0°C = 80 cal/g
m = Mass of water = 570 g
Heat removed for freezing

Let N be the number of cycles and each cycle removes 56 cal from the freezer.
So,

Each cycle takes 10 seconds so the total time would be

The total time taken to freeze 138.18 minutes
Answer:
B. Decrease the plane’s speed and height
Explanation:
Decrease in speed of plane:
When the speed of the plane is decreased then initial velocity of the package will be lesser. As a result, final velocity will also be lesser because in this case final velocity depends upon the initial velocity.
Decrease in height:
According to law of conservation of energy:
Loss in potential energy = Gain in Kinetic energy
mgh = ½ mV^2
It means with the decrease in height less potential energy will be converted to kinetic energy. As package has constant mass so it will gain less velocity.