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Vsevolod [243]
3 years ago
13

A slender rod of length 80.0 cm and 0.600 kg has its center of gravity at its geometrical center. But its density is not uniform

; it increases by the same amount from the center of the rod out to either end. You want to determine the moment of inertia Icm of the rod for an axis perpendicular to the rod at its center, but you don't know its density as a function of distance along the rod, so you can't use an integration method to calculate Icm. Therefore, you make the following measurements: You suspend the rod about an axis that is a distance d (measured in meters) above the center of the rod and measure the period T (measured in seconds) for small-amplitude oscillations about the axis. You repeat this for several values of d. When you plot your data as T2−4π2d/g versus 1/d, the data lie close to a straight line that has slope 0.470 m⋅s2. What is the value of Icm for the rod?
Physics
1 answer:
Vlad [161]3 years ago
7 0

Answer:

Icm = 0.0701 kgm^2

Explanation:

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A long, thin solenoid has 450 turns per meter and a radius of 1.17 cm. The current in the solenoid is increasing at a uniform ra
sergey [27]

Answer:

\frac{di}{dt}  = 7.31 \  A/s

Explanation:

From the question we are told that  

     The  number of turns is  N =  450 \  turns

      The  radius is  r =  1.17 \ cm =  0.0117 \ m

       The  position from the center consider is  x =  3.45 cm  =  0.0345 m

       The  induced emf is  e  =  8.20 *10^{-6} \  V/m

Generally according to Gauss law

        \int\limits { e } \, dl  =  \mu_o *  N  *  \frac{di}{dt }  *  A

=>    e *  2\pi x  =  \mu_o  *  N  *  \frac{d i }{dt }  *  A

Where A is the  cross-sectional area of the solenoid which is mathematically represented as

                A =  \pi r ^2

=>      e *  2\pi x  =  \mu_o  *  N  *  \frac{d i }{dt }  *  \pi r^2

=>       \frac{di}{dt}  =  \frac{2e * x  }{\mu_o * N  * r^2}ggl;

Here  \mu_o is the permeability of free space with value

          \mu_o  =  4\pi * 10^{-7} \  N/A^2

=>     \frac{di}{dt}  =  \frac{2 *  8.20*10^{-6} *  0.0345  }{ 4\pi * 10^{-7} * 450  * (0.0117)^2}

=>      \frac{di}{dt}  = 7.31 \  A/s

6 0
4 years ago
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