Q.9) Consider a plot of the displacement (x) as a function of the applied force (F) for an ideal elastic spring as shown, see figure. The slope of the curve would be
A) the acceleration due to gravity.
B) the reciprocal of the acceleration of gravity.
C) the mass of the object attached to the spring.
D) the reciprocal of the spring's constant.

Using the spring constant and displacement relation, the slope of the curve would be the reciprocal of the spring's constant.

Using the Force constant relation :

F = Force ; k = spring constant ; e = extension

Making the x the subject of the formula :

The slope, which is the spring constant can be expressed as ;

Hence, the slope is the reciprocal of the spring constant.

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Option (D).

Explanation:

For an ideal spring, the force is given in terms of displacement as follows :

F=-kx

...(1)

Where,

x is displacement in spring i.e. compression or stretching

k is spring constant of the spring

-ve sign shows that the force exerted by the spring is in opposite direction of the spring's displacement.

The equation of a line is : y=mx+c, m is slope

From equation (1)

Slope = 1/k

or

Slope = reciprocal of the spring's constant.

It would mean that the slope of the curve represents the reciprocal of the spring's constant.

the moving of the box is a result of centripetal force. think of that  as a car or a truck in this case creates a turn, the force of friction performing upon the turned wheels of the car runs centripetal force obligatory for circular motion for the things inside it.