Answer:
A) 12.57 m
B) 5 RPM
C) 3.142 m/s
Explanation:
A) Distance covered in 1 Revolution:
The formula that gives the relationship between the arc length or distance covered during circular motion to the angle subtended or the revolutions, is given as follows:
s = rθ
where,
s = distance covered = ?
r = radius of circle = 2 m
θ = Angle = 2π radians (For 1 complete Revolution)
Therefore,
s = (2 m)(2π radians)
<u>s = 12.57 m</u>
B) Angular Speed:
The formula for angular speed is given as:
ω = θ/t
where,
ω = angular speed = ?
θ = angular distance covered = 15 revolutions
t = time taken = 3 min
Therefore,
ω = 15 rev/3 min
<u>ω = 5 RPM</u>
C) Linear Speed:
The formula that gives the the linear speed of an object moving in a circular path is given as:
v = rω
where,
v = linear speed = ?
r = radius = 2 m
ω = Angular Speed in rad/s = (15 rev/min)(2π rad/1 rev)(1 min/60 s) = 1.571 rad/s
Therefore,
v = (2 m)(1.571 rad/s)
<u>v = 3.142 m/s</u>
Answer : The correct option is, (D) 278 K
Explanation :
We are given temperature
.
Now the conversion factor used for the temperature is,

where, K is kelvin and
is Celsius.
Now put the value of temperature, we get

Therefore, the temperature 278 K is equal to the 
The work done by the machine is equal to the product between the force applied and the distance over which the force is applieds, so in this case:

And the power of the machine is equal to the ratio between the work done by the machine and the time taken:
a) 1.48 m/s
The tuning fork is moving by simple harmonic motion: so, the maximum speed of the tip of the prong is related to the frequency and the amplitude by

where
is the maximum speed
is the angular frequency
A is the amplitude
For the tuning fork in the problem, we have
, where f is the frequency
is the amplitude
Therefore, the maximum speed is

b) 
The fly's maximum kinetic energy is given by

where
is the mass of the fly
is the maximum speed
Substituting into the equation, we find
