Question

189. Each of the two identical magnets, when suspended alone, makes 30 oscillations per minute at a place. The number of oscillations per minute, if they are fixed at right angles( to form a cross) and allowed to oscillate in the same field will be approximately 1. 25 oscillation/minute 2. 30 oscillation/minute 3. 60 oscillation/minute 4. 15 oscillation/minute.
​

Answer 1

Explanation:

Answer: Each of the two identical magnets, when suspended alone, makes 30 oscillations per minute at a place. The number of oscillations per minute, if they are fixed at right angles( to form a cross) and allowed to oscillate in the same field will be approximately 1. 25 oscillation/minute 2.

Answer 2

The number of oscillations per minute, if they are fixed at right angles( to form a cross) and allowed to oscillate in the same field will be approximately

We know, the Time period of a magnet oscillating in a horizontal magnetic field B is given by,

T = 2π$\sqrt{\frac{I}{MB} }$

Here, the magnetic field is same, so B will remain same.

So, T ∝ $\sqrt{\frac{I}{M}}$

Now, After making a cross (at right angle) with the two magnets,

I will be = 2I

M will be = √2

Now,

T₁/T₂ = $\sqrt{\frac{I/2I}{M/\sqrt{2}M } }$   [T₁ is the Time period of oscillation in the first case and                                    

                              T₂ is  the Time period of oscillation in the second case]

or, T₁/T₂ = $\sqrt\frac{\sqrt{2} }{2} }$

or, T₁/T₂  = 2⁻¹/⁴

or, T₂ = T₁ × 2¹/⁴

or, T₂ = 30 × 2¹/⁴ [As T₁  is given 30 oscillations per minute]

or, T₂ ≅ 35 oscillations per minute

The nearest value given in the options is 30, so, the answer will be 30 oscillations/minute.