Ahollow sphere of radius 0.200 m, with rotational inertia i = 0.0484 kg·m2 about a line through its center of mass, rolls without slipping up a surface inclined at 27.1° to the horizontal. at a certain initial position, the sphere's total kinetic energy is 20.0 j. (a) how much of this initial kinetic energy is rotational? (b) what is the speed of the center of mass of the sphere at the initial position? when the sphere has moved 0.900 m up the incline from its initial position, what are (c) its total kinetic energy and (d) the speed of its center of mass?

Part a)

Part b)

v = 3.64 m/s

Part c)

Part d)

Explanation:

As we know that moment of inertia of hollow sphere is given as

here we know that

R = 0.200 m

now we have

now we know that total Kinetic energy is given as

Part a)

Now initial rotational kinetic energy is given as

Part b)

speed of the sphere is given as

v = 3.64 m/s

Part c)

By energy conservation of the rolling sphere we can say

Part d)

Now we know that

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation: