Two uniform bars of the same dimensions are constructed from the same material. One bar has five evenly spaced holes through it and the second bar has only two holes. In these cases, the bars are slid over vertical pegs and rest on a horizontal surface, where friction between the bar and the surface is negligible. The two bars are each pulled by horizontal forces of equal magnitude F from their right end as shown above. The bars' resulting angular accelerations are recorded.

Is the magnitude of the initial angular acceleration of the bar in case 1 larger than, smaller than or equal to the magnitude of the initial angular acceleration of the bar in Case 2? Explain your reasoning.

Solution :

The angular acceleration, is obtained from the equation of the of rotational motion,

Thus,

or

where is torque, F is force, d is moment arm distance, I is the moment of inertia

Thus,

Now if the force and the moment arm distance are constant, then the

That is when, F = d = constant, then   .

Thus, moment of inertia, I is proportional to mass of the bar.

The mass is less for the bar in case (1) in comparison with that with the bar in case (2) due to the holes that is made in the bar.

Therefore, the bar in case (1), has less moment of inertia and a greater angular acceleration.

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.

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