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:
E. Student 1 is correct, because as θ is increased, h is the same.
Explanation:
Here we have the object of a certain mass falling under gravity so the force acting on the it will depend on mass of the object and the acceleration due to gravity.
Mathematically:

As we know that the work done is evaluated as the force applied on a body and the displacement of the body in the direction of the force.
And for work we have:

where:
displacement of the object
angle between the force and displacement vectors
Given that the height of the object is same in each trail of falling object under the gravity be it a free-fall or the incline plane.
- In case of free-fall the angle between the force is and the displacement is zero.
- In case when the body moves along the inclined plane the force applied by the gravity is same because it depends upon the mass of the object. And the net displacement in the direction of the gravitational force is the height of the object which is constant in both the cases.
So, the work done by the gravitational force is same in the two cases.
New substances are formed by chemical reactions. When elements react together to form compounds their atoms join to other atoms using chemical bonds. For example, iron and sulfur react together to form a compound called iron sulfide. Hopefully this will help you decide...
Answer:
distance = 3 + 4 = 7 mi
displacement is √(3² + 4²) = 5 mi
Explanation: