Answer:
The work done by the hoop is equal to 5.529 Joules.
Explanation:
Given that,
Mass of the hoop, m = 96 kg
The speed of the center of mass, v = 0.24 m/s
To find,
The work done by the hoop.
Solution,
The initial energy of the hoop is given by the sum of linear kinetic energy and the rotational kinetic energy. So,

I is the moment of inertia, 
Since, 


Finally it stops, so the final energy of the hoop will be, 
The work done by the hoop is equal to the change in kinetic energy as :

W = -5.529 Joules
So, the work done by the hoop is equal to 5.529 Joules. Therefore, this is the required solution.
Answer : The number of half-life periods will be, 3
Explanation : Given,
Initial amount of lead = 10 kg
Amount of lead after decay = 1.25 kg
Half-life = 22 years
Formula used :

where,
a = amount of reactant left after n-half lives
= Initial amount of the reactant
n = number of half lives
= half-life
Now put all the given values in the above formula, we get:




Thus, the number of half-life periods will be, 3
Answer:
The velocity of block = 0.188 
Explanation:
Mass m = 5.6 kg
k = 1040 
= 0.26
0.035 m ,
= 0
0.02 m
From work energy theorem
--------- (1)
Kinetic energy
------- (1)
Potential energy
------- (2)
Work done
W = F.s ------ (3)
From Newton's second law
= mg
= 5.6 × 9.81 = 54.9 N
Friction force = 0.4 × 54.9 = 21.9 N
Now the work done by the friction
= - 21.9 × 0.015
= - 0.329 J
Now kinetic energy
At point 1




0.637 J
At point 2


Potential energy


J
From equation (1) we get
0 + 0.637 - 0.329 = 2.8
+ 0.208
2.8
= 0.1
0.188 
This is the velocity of block.
Answer:
Electromagnetic waves differ from mechanical waves in that they do not require a medium to propagate. This means that electromagnetic waves can travel not only through air and solid materials, but also through the vacuum of space.
Explanation:
Since electromagnetic waves do not require a medium to pass through, they are faster in matter that has fewer particles. ... ~ Sound cannot travel in a vacuum because mechanical waves, such as sound waves, require a medium to propagate through.