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At a certain place, a magnet makes 30 oscillations per minute. At another place where the magnetic field is doubled, its time period will be
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Verified Answer
The correct answer is:
$\sqrt{2} \mathrm{~s}$
Time period of magnet in magnetic field
$$
T \propto \frac{1}{\sqrt{B}}
$$
If magnetic field is doubled, then
$$
\begin{aligned}
& T^{\prime} \propto \frac{1}{\sqrt{2 B}} \\
& \Rightarrow \quad T^{\prime} \propto \frac{T}{\sqrt{2}}=\frac{2}{\sqrt{2}}=\sqrt{2} \mathrm{~s} \\
&
\end{aligned}
$$
$$
\text { [oscillation per second }=\frac{30}{60} \text { ] }
$$
$$
T \propto \frac{1}{\sqrt{B}}
$$
If magnetic field is doubled, then
$$
\begin{aligned}
& T^{\prime} \propto \frac{1}{\sqrt{2 B}} \\
& \Rightarrow \quad T^{\prime} \propto \frac{T}{\sqrt{2}}=\frac{2}{\sqrt{2}}=\sqrt{2} \mathrm{~s} \\
&
\end{aligned}
$$
$$
\text { [oscillation per second }=\frac{30}{60} \text { ] }
$$
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