A sphere of radius 10.0cm is moulded into a uniform cylindrical wire of same radius r calculate length in millimeters

133.33 mm

Explanation:

First we need to find the volume of the sphere. The volume of a sphere is given by:

V = (4/3) * pi * r^3

With a radius of 10 cm, we have:

V = (4/3) * pi * r^3 = 4188.79 cm3

The sphere will be moulded into a cylinder, so the volume will be the same. The volume of a cylinder is:

V = pi * r^2 * h

Where h is the height of the cylinder, and for this case, it will be the length.

The radius is the same old radius, so we have:

4188.79 = pi * 10^2 * h

h = 4188.79 / 100pi = 13.3333 cm

In millimeters, we have h = 133.33 mm

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft