i think its B)... im not sure so dont take it seriously
Answer:
(a) 
(b) 
Explanation:
Given data
The angular velocity of two cylinders ω=257 rad/s
The mass of the two cylinders m=2.88 kg
The radius of small cylinder r₁=0.319 m
The radius of larger cylinder r₂=0.605 m
For Part (a)
The rotational kinetic energy of the cylinder is given by:

Where I is rotational of inertia of solid cylinder about its central axis.
So

Substitute the given values
So

For Part (b)

Substitute the given values

The centripetal acceleration of an object is given by the relation,

where Ac = centripetal acceleration =
R = radius of rotation = 15 m
V = speed of astronaut
Hence, 
solving this we get, V = 38.34 m/s
Answer:
Spring constant of the spring will be equal to 9.255 N /m
Explanation:
We have given mass m = 0.683 kg
Time taken to complete one oscillation is given T = 1.41 sec
We have to find the spring constant of the spring
From spring mass system time period is equal to
, here m is mass and K is spring constant
So 

Squaring both side


So spring constant of the spring will be equal to 9.255 N /m