Two wheels roll side-by-side without sliding, at the same speed. The radius of wheel 2 is one-half (1/2) the radius of wheel 1. The angular velocity of wheel 2 is:

w'=(1/2)w

Explanation:

In order to calculate the angular velocity of the second wheel, you use the following formula:

     (1)

v: speed of the wheel 1 = speed of the wheel 2

r: radius of the wheel 1

For the second wheel you have:

r'=2r

You replace this value of r' in the following equation:

The angular velocity of the second wheel is one half of the angular velocity of the first wheel

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