Answer:


Explanation:
Here mass density of rod is varying so we have to use the concept of integration to find mass and location of center of mass.
At any distance x from point A mass density


Lets take element mass at distance x
dm =λ dx
mass moment of inertia

So total moment of inertia

By putting the values

By integrating above we can find that

Now to find location of center mass


Now by integrating the above


So mass moment of inertia
and location of center of mass 
Number 4 is c , number 5 is a , number 6 is d and 7 is a
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This question deals with the law of conservation of momentum, which basically says that the total momentum in a system must stay the same, provided there are no outside forces. Since you were given the mass and velocity of the two objects you can find the momentum (p=mv) of each and then add them together to find the total momentum of the system before they collide. This total momentum must be the same after they collide. Since you have the mass and velocity of one of the objects after the collision you can find the its momentum after. Subtract this from the the system total and you will have the momentum of the other object after the collision. Now that you know the momentum of the other object you can find its velocity using p=mv and its mass from before.
Be careful with the velocities. They are vectors, so direction matters. Typically moving to the right is positive (+) and moving to the left is negative (-). It is not clear from your question which direction the objects are moving before and after the collision.
Answer:
6KW
Explanation:
The computation is shown below:
We know that
Work done= m ×g× h
Here
W= 300×10×10
= 30000 J
= 30 KJ
And
Power= Work done ÷time taken
P = 30000 ÷ 5
= 6000W
= 6KW
The above represent the answer