In an experiment, a solid, uniform sphere is at rest on a horizontal surface. A net force is applied tangentially to the edge of the sphere that is the greatest horizontal distance away from the central axis of the sphere. The sphere begins to rotate from rest until the force is no longer applied after 3s. Frictional forces between the sphere and the horizontal surface are considered to be negligible. Which two of the following quantities, when used together, could a student measure to determine the change in angular momentum of the sphere from 0s to 3s.
a. Radius of the sphere
b. The volume of the sphere
c. Average angular acceleration of the sphere from 0 to 3s
d. Average net force exerted on the sphere from 0 to 3s

Option A and D

Radius of the sphere, and,

Average net force exerted on the sphere from 0 to 3s

Explanation:

The product of the average net force and the radius will give the torque

T = F x r

The product of torque and time will give the change in angular momentum

T x t = I2w2 - I1w1

Where F is the average force,

r is the radius,

T is the torque,

t is the time (0 to 3sec)

I = moment of inertia of the system

w is the angular speed.

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.