Acertain string can withstand a maximum tension of 39. n without breaking. a child ties a 0.43 kg stone to one end and, holding the other end, whirls the stone in a vertical circle of radius 0.98 m, slowly increasing the speed until the string breaks. where is the stone on its path when the string breaks (top of the circle, middle of the circle or bottom of the circle)

Bottom of the circle.

Explanation:

At the top of the circle the tension and the weight contribute on being the centripetal force, at the middle of the circle only the tension contributes on being the centripetal force (the weight being perpendicular to it), while at the bottom of the circle the tension contributes on being the centripetal force (as always) but the weight against to it, so here is where the tension must be greater to allow the same centripetal force as the other cases, thus here is where the string will break.

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards