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In a vibration magnetometer, the time-period of magnets when the identical poles are in the same directon is 3 s. When the polarity of weaker magnet is reversed, the combination makes 15 oscillations per minute. The ratio of magnetic moments of the magnets is
  • a)
    9:16
  • b)
    16:9
  • c)
    7:25
  • d)
    25:7
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
In a vibration magnetometer, the time-period of magnets when the ident...
Solution:

Given, time-period of magnets with identical poles = 3 s

Let the magnetic moments of the two magnets be M1 and M2, where M1 is stronger than M2.

When the weaker magnet is reversed, the combination makes 15 oscillations per minute.

Let the time-period of the combination be T.

We know that time-period is inversely proportional to the square root of magnetic moment.

∴ T ∝ 1/√(M1 + M2) …(1)

Also, T ∝ 1/√(M1 – M2) …(2)

From equations (1) and (2), we get:

√(M1 + M2) ∝ 1/√(M1 – M2)

M1 + M2 = k/(M1 – M2) …(3), where k is a constant of proportionality.

When identical poles are in the same direction, the time-period is given as:

T’ = 2π√(M1M2)/(M1 + M2)

Substituting the value of T’ as 3 s, we get:

3 = 2π√(M1M2)/(M1 + M2)

∴ M1M2/(M1 + M2) = 9π^2 …(4)

When the weaker magnet is reversed, the time-period becomes:

T’’ = 60/15 = 4 s

Substituting the value of T’’ in equation (1), we get:

4 ∝ 1/√(M1 + M2)

(M1 + M2) = 16 …(5)

Solving equations (4) and (5), we get:

M1/M2 = 25/7

Therefore, the ratio of magnetic moments of the magnets is 25:7 (Option D).
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In a vibration magnetometer, the time-period of magnets when the identical poles are in the same directon is 3 s. When the polarity of weaker magnet is reversed, the combination makes 15 oscillations per minute. The ratio of magnetic moments of the magnets isa)9:16b)16:9c)7:25d)25:7Correct answer is option 'D'. Can you explain this answer?
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