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
⇒ 

=
+ 

⇒

'Universe' means 'Everything'. That is, all matter, all space, all time.
The correct answer is c because B) is a vector which includes both velocity and direction
Answer:
Total kinetic energy of entire system is 3 mgl
Explanation:
Given two masses: m and 4m.
Since the pulley is frictionless and the thread is massless, the energy here is linked to the two masses.
Total kinetic energy of entire system = decrease in gravitational potential energy of the system.
Therefore, we have :
ΔKE = Δp
ΔKE = 4mgl - mgl
= 3 mgl
Total kinetic energy of entire system is 3 mgl