JEE Main 2021 · 20 July · evening · Single correct · +4 / −1
At an angle of 30° to the magnetic meridian, the apparent dip is 45°. Find the true dip :
- (a) tan ⁻¹√3
- (b) tan ⁻¹1/√3
- (c) tan ⁻¹2/√3
- (d) tan ⁻¹√3/2
Answer and solution
Answer (d) tan ⁻¹√3/2
Solution
Physics sir · 3 steps
Turn the dip circle off the meridian and only H gets weaker, so the apparent dip is always the steeper one.
- What changes. In a vertical plane at angle θ to the magnetic meridian, the vertical component V acts fully on the needle. Only the part of H along that plane acts, which is H cos θ.
tan δ' = V/(H cos θ) = (tan δ)/(cos θ)
- Put in numbers. Here δ' = 45° and θ = 30°. So tan δ = tan 45° × cos 30° = 1 × √3/2 = √3/2.
- So. The true dip is δ = tan⁻¹√3/2, which is option (d).
The idea to keep. Off the meridian, V stays the same and H becomes H cos θ. So tan δ' = tan δ/cos θ, and the true dip is always smaller than the apparent dip.
Answer from the NTA final answer key. Solution by PrepWiser.