A magnet is suspended in such a way that it oscillates in a horizontal plane- It makes 60 oscillations in 2 minutes at a point where dib angle is 30- and 30 oscillations in 2 minutes at a point where dip angle is 60- The ratio of magnetic field at two places is-

The correct option is D 4 : 3T = 2 π√(I/MH) = 2π√(I/MB cos δ) T_1/T_2 = √(B_2 cos δ_2/B_1 cos δ_1) = √(B_2/B_1cos δ_2/cos δ_1) B_2/B_1cos δ_2/cos δ_1 = T_1 ...

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Byju's Answer

Standard XII

Physics

Solenoid Core in Magnetic Field

A magnet is s...

Question

A magnet is suspended in such a way that it oscillates in a horizontal plane. It makes 60 oscillations in 2 minutes at a point where dib angle is $30^{\circ}$ and 30 oscillations in 2 minutes at a point where dip angle is $60^{\circ}$ . The ratio of magnetic field at two places is.

2 : 1

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4 : 3

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3 : 2

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5 : 4

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Solution

The correct option is B 4 : 3
$T = 2 π \sqrt{\frac{I}{M H}} = 2 π \sqrt{\frac{I}{M B c o s δ}}$
$\frac{T_{1}}{T_{2}} = \sqrt{\frac{B_{2} c o s δ_{2}}{B_{1} c o s δ_{1}}} = \sqrt{\frac{B_{2}}{B_{1}} \frac{c o s δ_{2}}{c o s δ_{1}}}$
$\frac{B_{2}}{B_{1}} \frac{c o s δ_{2}}{c o s δ_{1}} = \frac{T_{1}^{2}}{T_{2}^{2}}$
$\frac{B_{2}}{B_{1}} = \frac{T_{1}^{2} c o s δ_{1}}{T_{2}^{2} c o s δ_{2}} = \frac{1}{4} \times \frac{c o s^{2} 30}{c o s^{2} 60}$
$= \frac{1}{4} \times \frac{\frac{3}{4}}{\frac{1}{3}} = \frac{3}{4}$
$\frac{B_{1}}{B_{2}} = \frac{4}{3}$

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A magnet is suspended in such a way that it oscillates in a horizontal plane. It makes 60 oscillations in 2 minutes at a point where dib angle is 30∘ and 30 oscillations in 2 minutes at a point where dip angle is 60∘. The ratio of magnetic field at two places is.

The correct option is B 4 : 3T=2π√IMH=2π√IMB cos δ T1T2=√B2 cos δ2B1 cos δ1=√B2B1cos δ2cos δ1 B2B1cos δ2cos δ1=T21T22 B2B1=T21 cos δ1T22 cos δ2=14×cos230cos260 =14×3413=34 B1B2=43

A magnet is suspended in such a way that it oscillates in a horizontal plane. It makes 60 oscillations in 2 minutes at a point where dib angle is $30^{\circ}$ and 30 oscillations in 2 minutes at a point where dip angle is $60^{\circ}$ . The ratio of magnetic field at two places is.