Aspool is placed on table top. the static friction coefficient between the table top and the spool is high.
part (a) if the string is pulled out over the bottom of the axle as shown, in which direction will the spool roll?
multiplechoice :
1) in the same direction as the applied force.
2) it depends on how much force is applied.
3) it will stay in one place and spin.
4) in the opposite direction of the applied force.

1) In the same direction as the applied force.

Explanation:

As we can see the figure the force is applied on the string to pull the string towards us.

Now as we know that friction is sufficient high so that contact point will not slide here and always remains at rest

So here the applied force will be the only force which will exert the torque on the cylinder about the bottom contact point of the cylinder with the ground.

So here the rotation of the cylinder will be due to this torque and it will be in the direction of applied force only

c) up

hope this

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .