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Transverse waves are being generated on a rope under constant tension. Determine the factor by which the required power is changed in each of the following situations.
(a) Both the length of the rope and the wavelength are halved.
(b) The length of the rope is doubled, and the angular frequency remains constant.
(c) Both the wavelength and the amplitude are doubled.
(d) The amplitude is doubled, and the angular frequency is halved.
A sphere of radius R is uniformly charged to a total charge of Q. It is made to spin about an axis that passes through its center with an angular speed ω. Find the magnitude of the resulting magnetic field at the center of the sphere.
A resistor is in the shape of a cube, with each side of resistance R . Find the equivalent resistance between any two of its adjacent corners.
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