Academic Experts Solutions for Chapter: Magnetism and Matter, Exercise 5: Bar Magnet

A dip needle lies initially in the magnetic meridian when it shows an angle of dip $\mathrm{\theta }$ at a place. The dip circle is rotated through an angle $x$ in the horizontal plane and then it shows an angle of dip $\theta \text{'}$. Then, $\frac{\tan \theta \text{'}}{\tan \theta }$is,

A dip needle vibrates in the vertical plane perpendicular to the magnetic meridian. The time period of vibration is found to be $2 s$. The same needle is then allowed to vibrate in the horizontal plane and the time period is again found to be $2 s$. Then the angle of dip is

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

The true value of angle of dip at a place is $60°$. The apparent dip in a plane inclined at an angle of $30°$ with magnetic meridian is 

If ${\mathrm{\varphi }}_1$ and ${\mathrm{\varphi }}_2$ be the angles of dip observed in two vertical planes at right angles to each other and $\mathrm{\varphi }$ be the true angle of dip, then

A dip circle is adjusted so that its needle moves freely in the magnetic meridian. In this position, the angle of dip is $40°$. Now the dip circle is rotated so that the plane in which the needle moves makes an angle of $30°$ with the magnetic meridian. In this position the needle will dip by an angle

If the angle of dip at two places are $30°$ and $45°$ respectively, then the ratio of horizontal component of earth's magnetic field at two places will be 

The value of earth magnetic field $B_H=0.3 \mathrm{G}$. In this magnetic field a magnet is oscillating with $5 \mathrm{oscillations} {\min }^{-1}$. To increase the oscillation of magnet upto $10 \mathrm{oscillations} {\min }^{-1}$, the value of earth magnetic field is increased by