Question

A magnet is suspended in such a way that it oscillates in the horizontal plane. If it makes 20 oscillations per minute at a place where dip angle is 30${}^0$ and 15 oscillations per minute at a place where dip angle is 60${}^0$.The ratio of total earth's magnetic field at the two places is :

• A. $3\sqrt{3}:8$
• B. $16:9\sqrt{3}$
• C. 4:9
• D. $2\sqrt{3}:9$

Answer 1

Answer: (B)

$16:9\sqrt{3}$

${\theta }_1={30}^0$
${\theta }_2={60}^0$
${\omega }_1=20$ osc/min
${\omega }_2=15$ osc/min

$\frac{1}{2}I\omega {{}_1}^2=m{I}_1\cos {\theta }_1$ . ......(1)

$\frac{1}{2}I\omega {{}_2}^2=m{I}_2\cos {\theta }_2$ ........(2)
(1) $÷$(2)

$\frac{{\left(20\right)}^2}{{\left(15\right)}^2}=\frac{I_1\cos {30}^0}{I_2\cos {60}^0}$
or, $\frac{I_1}{I_2}=\frac{16}{9\sqrt{3}}$