The mass of the bird is 0.32 kg.
<u>Explanation:</u>
Gravitational potential energy, the energy exhibited by an object at rest due to the influence of gravitational force. So the increase in distance of object from the surface of earth leads to increase in the gravitational potential energy. Thus,

So, as the gravitational potential energy is given as 2033 J and the position of bird placed on the tall tower is 639 m away from the bottom, then the mass (m) of the bird can be found as below.

So, finally we get the bird's mass as,
m of bird = 0.32 kg
The mass on the spring is 0.86 kg
Explanation:
The period of a mass-spring system is given by the equation

where
m is the mass
k is the spring constant
In this problem, we have:
k = 88.7 N/m is the spring constant
The system makes 15 oscillations in 9.24 s: therefore, the period of the system is

Now we can re-arrange the first equation to solve for the mass:

Learn more about period:
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Answer:
M
Explanation:
To apply the concept of <u>angular momentum conservation</u>, there should be no external torque before and after
As the <u>asteroid is travelling directly towards the center of the Earth</u>, after impact ,it <u>does not impose any torque on earth's rotation,</u> So angular momentum of earth is conserved
⇒
-
is the moment of interia of earth before impact -
is the angular velocity of earth about an axis passing through the center of earth before impact
is moment of interia of earth and asteroid system
is the angular velocity of earth and asteroid system about the same axis
let 
since 

⇒ if time period is to increase by 25%, which is
times, the angular velocity decreases 25% which is
times
therefore

(moment of inertia of solid sphere)
where M is mass of earth
R is radius of earth

(As given asteroid is very small compared to earth, we assume it be a particle compared to earth, therefore by parallel axis theorem we find its moment of inertia with respect to axis)
where
is mass of asteroid
⇒ 

=
+ 

⇒

Answer:
K = 373.13 N/m
Explanation:
The force of the spring is equals to:
Fe - m*g = 0 => Fe = m*g
Using Hook's law:
K*X = m*g Solving for K:
K = m/X * g
In this equation, m/X is the inverse of the given slope. So, using this value we can calculate the spring's constant:
K = 10 / 0.0268 = 373.13N/m