/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 11 A magnet makes 30 oscillations p... [FREE SOLUTION] | 91影视

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Chapter 15: Problem 11

A magnet makes 30 oscillations per minute at a plane where intensity is \(32 \mathrm{~T}\). At another place it takes \(1 \mathrm{~s}\) to complete one oscillation. The value of horizontal intensity at the second place is, (A) \(12.8 \mathrm{~T}\) (B) \(25.6 \mathrm{~T}\) (C) \(128 \mathrm{~T}\) (D) \(256 \mathrm{~T}\)

Short Answer

Expert verified
The value of horizontal intensity at the second place is \(128 \mathrm{T}\), which corresponds to option (C).

Step by step solution

01

Calculate the Time Period of oscillations at the first place

Since the magnet oscillates 30 times in a minute, we can find the time period (T1) for one oscillation at the first place by dividing 60 seconds by the number of oscillations, which is 30 times. T1 = 60 seconds / 30 oscillations
02

Apply the formula for Time Periods of oscillations

For a magnet oscillating in a magnetic field, the time period (T) is directly proportional to the square root of the magnetic field intensity (H). The formula to relate these quantities is given as follows: \(T = 2\pi \sqrt{\frac{I}{H}}\) In our case, at the first place, T1 and H1 are given, and at the second place, T2 and H2 should be found. We'll use the above formula to establish the relationship between T1, H1, and T2, H2.
03

Use the formula to relate T1, H1, and T2, H2

We have the following equation for the first place (T1, H1): \(T1 = 2\pi \sqrt{\frac{I}{H1}}\) For the second place (T2, H2): \(T2 = 2\pi \sqrt{\frac{I}{H2}}\) Now, we have two equations with two unknowns, I and H2. We can use these equations to get the value of H2.
04

Express I in H1 and H2

Divide the equation for the second place by the equation for the first place: \(\frac{T2}{T1} = \frac{2\pi \sqrt{\frac{I}{H2}}}{2\pi \sqrt{\frac{I}{H1}}}\) Simplify the equation by cancelling out \(2\pi\) and I: \(\frac{T2}{T1} = \sqrt{\frac{H1}{H2}}\) Now, we can find H2 knowing the values of T1, T2, and H1.
05

Calculate the value of H2

Given the values of T1, T2 and H1: T1 = 2 seconds (from Step 1), T2 = 1 second (given), H1 = 32 T (given) Now, we can find the value of H2 by using the equation from Step 4. \(\frac{T2}{T1} = \sqrt{\frac{H1}{H2}}\) Substitute the values of T1, T2 and H1 into the equation: \(0.5 = \sqrt{\frac{32}{H2}}\) Square both sides of the equation: \(0.25 = \frac{32}{H2}\) Solve for H2: \(H2 = \frac{32}{0.25} = 128\ T\) The value of horizontal intensity at the second place is 128 T, which corresponds to option (C).

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