SATHEE: Magnetism and Matter - Result Question 11

Magnetism and Matter - Result Question 11

15. If $θ_{1}$ and $θ_{2}$ be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of $d i p θ$ is given by :-

(a) $\tan^{2} θ = \tan^{2} θ_{1} + \tan^{2} θ_{2}$

[2017]

(b) $\cot^{2} θ = \cot^{2} θ_{1} - \cot^{2} θ_{2}$

(d) $\cot^{2} θ = \cot^{2} θ_{1} + \cot^{2} θ_{2}^{2}$

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Answer:

Correct Answer: 15. (d)

Solution:

(d) If $θ_{1}$ and $θ_{2}$ are opparent angles of dip Let $α$ be the angle which one of the plane make with the magnetic meridian.

$\tan θ_{1} = \frac{v}{H \cos α}$

i.e., $\cos α = \frac{v}{H \tan θ_{1}}$

$\tan θ_{2} = \frac{v}{H \sin α}$ ,

i.e., $\sin α = \frac{v}{H \tan θ_{2}}$

Squaring and adding (i) and (ii), we get

$\cos^{2} α + \sin^{2} α = (\frac{V}{H})^{2} (\frac{1}{\tan^{2} θ_{1}} + \frac{1}{\tan^{2} θ_{2}})$ i.e., $1 = \frac{V^{2}}{H^{2}} [\cot^{2} θ_{1} + \cot^{2} θ_{2}]$

or $\frac{H^{2}}{V^{2}} = \cot^{2} θ_{1} + \cot^{2} θ_{2}$

i.e., $\cot^{2} θ = \cot^{2} θ_{1} + \cot^{2} θ_{2}$

Magnetism and Matter - Result Question 11

15. If $θ_{1}$ and $θ_{2}$ be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of $d i p θ$ is given by :-

Answer:

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Magnetism and Matter - Result Question 11

15. If θ1 and θ2 be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dipθ is given by :-

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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15. If $θ_{1}$ and $θ_{2}$ be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of $d i p θ$ is given by :-