A 0.74-m diameter solid sphere can be rotated about an axis through its center by a torque of 10.8 m*N which accelerates it uniformly from rest through a total of 160 revolutions in 14.0 s.
1. What is the mass of the sphere?

Mass of the sphere is 19.2 kg

Explanation:

We have given diameter of the sphere d = 0.74 m

So radius r = 0.37 m

Initial angular velocity

Time t = 14 sec

Angular displacement

From second equation of motion

So

Torque is given

Torque is equal to , here I is moment of inertia and angular acceleration

So

Moment of inertia of sphere is equal to

So

M = 19.23 kg

So mass of the sphere is 19.23 kg

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.

i think its c if i'm wrong