please help with these An LC circuit has a resonance frequency of 90 kHz, If the

Question

please help with these

An LC circuit has a resonance frequency of 90 kHz, If the inductor in the circuit has a value of 80 H, what is the capacitance of the circuit? 0.04 pF 1.5 pF 39 pF 4.4 pF An electron enters a magnetic field of 0.75 T with a velocity perpendicular to the direction of the field. At what frequency does the electron traverse a circular path? (The mass of an electron is 9.1 times 10^-31 kg, and the charge of an electron is 1.6 times 10^-19C) 4.8 times 10^-11 Hz 2.1 times 10^14 Hz 2.1 times 10^10 Hz 4.8 times 10^-7 Hz A spaceship is moving in a straight line at a speed of 0.8 c (relative to Earth). It launches a missile that moves away from the spaceship (traveling in the same direction as the spaceship) at a speed of 0.6 c. Relative to Earth, the speed of the missile is 1.4 c. greater than c and less than 1.4 c. greater than 0.8 c and less than c. c. A spaceship is moving between two distant stars at 0.932c. To someone in the ship, the distance between the two stars appears to be 26.9 ly. What is the distance between the stars in the stars' rest frame? 21.5 ly 74.2 ly 56.5 ly 9.75 ly

Explanation / Answer

9.

resonant frequency is, f = (1/2)[1/(LC)1/2]

or, C = 1/(4L2f2)

or, C = 1/(4X8HX(3.14)2X(9X103Hz)2)

or, C = 39pF

So, the correct option is the third one.

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10.

r = mv/qB

frequency is,

f = v/2r = qB/2m = (1.6X10-19C)(0.75 T)/(6.28X9.1X10-31kg)

or, f = 2.1X1010 Hz

So, the correct option is the third one.

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11.

the speed of the missile will be greater than 0.8c but less than c.

So correct option is the third one.

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12.

Let the distance in star's rest frame be L

then, L' = L(1 - v2/c2)1/2

or, 26.9y = L(1 - (0.932c)2/c2)1/2

or, L = 74.2 ly

So, the correct option is the 2nd one.

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This concludes the answers. Check the answer and let me know if it's correct. If you need any more clarification, modification or correction, feel free to ask.....

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