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:
a. b- x= y
dx = -dy
b. F = 
c. F = 
Explanation:
a. x components:

= 
Integrating and solving gives:
b- x= y
dx = -dy
b. the force is given by the equation derived from (a.):
F = 
c. Given that r>>a, the expression becomes:
F = 
Explanation:
When the size of the charge distribution is less than the distance to the deviation point of the charge then the charge distribution would produce the same effect such as a linear charge.
heat from water goes into air in ball
air expands
ping goes the dent
Answer: 0.2m
Explanation: Firstly only the Rocket's Weight Compress the spring which can be found by

According to Hooks Law

The part b and c of this question is done in the attachment