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ruslelena [56]
2 years ago
9

A particular planet has a moment of inertia of 9.74 × 1037 kg ⋅ m2 and a mass of 5.98 × 1024 kg. Based on these values, what is

the planet's radius? Hint: Because planets are the shape of a sphere, the moment of inertia is I = (2/5)mr2.
A) 6.38 x 106 m
B) 2.55 × 106 m
C) 6.52 × 1012 m
D) 4.07 × 1013m
Physics
1 answer:
malfutka [58]2 years ago
4 0

Answer:  A) 6.38(10)^{6} m

Explanation:

The equation for the moment of inertia I of a sphere is:

I=\frac{2}{5}mr^{2} (1)

Where:

I=9.74(10)^{37}kg m^{2} is the moment of inertia of the planet (assumed with the shape of a sphere)

m=5.98(10)^{24}kg is the mass of the planet

r is the radius of the planet

Isolating r from (1):

r=\sqrt{\frac{5I}{2m}} (2)

Solving:

r=\sqrt{\frac{5(9.74(10)^{37}kg m^{2})}{2(5.98(10)^{24}kg)}} (3)

Finally:

r=6381149.077m \approx 6.38(10)^{6} m

Therefore, the correct option is A.

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Which change will always result in an increase in the gravitational force between two objects?
aleksklad [387]

Answer:

increasing the masses of the objects and increasing the distance between the objects

8 0
3 years ago
If an earthquake occurred in Miami, Florida, then how long would it take for a seismic station in Seattle, Washington, to pick u
Juliette [100K]

0.017s

Explanation:

Given parameter

Distance = 5000km = 5 x 10⁶m

Unknown:

time taken = ?

Solution:

We use the normal speed equation to solve this problem as we take the speed of the wave to be 3 x 10⁸m/s.

   Speed = \frac{Distance }{Time taken}

   Inputting the parameters:

             Time taken = \frac{distance }{velocity of the wave}

  Time taken = \frac{ 5 000000}{3 00000000} = 0.017s

Learn more:

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8 0
2 years ago
A disk of mass m and moment of inertia of I is spinning freely at 6.00 rad/s when a second identical disk, initially not spinnin
Nadusha1986 [10]

Answer:

The angular speed of the new system is 3\,\frac{rad}{s}.

Explanation:

Due to the absence of external forces between both disks, the Principle of Angular Momentum Conservation is observed. Since axes of rotation of each disk coincide with each other, the principle can be simplified into its scalar form. The magnitude of the Angular Momentum is equal to the product of the moment of inertial and angular speed. When both disks begin to rotate, moment of inertia is doubled and angular speed halved. That is:

I\cdot \omega_{o} = 2\cdot I \cdot \omega_{f}

Where:

I - Moment of inertia of a disk, measured in kilogram-square meter.

\omega_{o} - Initial angular speed, measured in radians per second.

\omega_{f} - Final angular speed, measured in radians per second.

This relationship is simplified and final angular speed can be determined in terms of initial angular speed:

\omega_{f} = \frac{1}{2}\cdot \omega_{o}

Given that \omega_{o} = 6\,\frac{rad}{s}, the angular speed of the new system is:

\omega_{f} = \frac{1}{2}\cdot \left(6\,\frac{rad}{s} \right)

\omega_{f} = 3\,\frac{rad}{s}

The angular speed of the new system is 3\,\frac{rad}{s}.

6 0
2 years ago
20. In a parallel RL circuit, 10 mA flows through the resistor and 4 mA flows through the inductor. What phase angle separates v
stellarik [79]

Answer:

Option D: 21.8 degrees

Explanation:

In a parallel RL circuit, the current in the resistor R and that in the inductor L are separated among themselves 90 degrees as illustrated in the attached image. In the image the current in the resistor is represented in orange, that of the inductor in blue, and the total current (vector addition of the previous two) is represented  in red, forming a certain angle (theta) with respect to the current in the resistor. The output voltage is the same as the input voltage as measured over the resistor R.

Therefore, the phase angle that separated output voltage and total current can be obtained using the fact that tan(phase angle) = \frac{I_l}{I_R} = \frac{x}{y} \frac{4}{10}, therefore the angle is the arctangent of 4/10:

arctang(\frac{4}{10} )= 21.801 degrees.

8 0
3 years ago
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Need help with exercises 3,4,5<br><br> Will give brainliest!!!
Harman [31]

I pretty sure that 3 is b and 4 is A and 5 I need a full picture

4 0
3 years ago
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