A magnetic compass needle oscillates 30 times per minute at a place where the dip is 45 ° and 40 times per minute where the dip is 30 ° . If B 1 and B 2 are the net magnetic fields due to the earth at the two places respectively, then the ratio B 1 / B 2 is approximately equal to

Step-by-step solution

Let f 1 and f 2 be the respective oscillation frequencies respectively for 45 ° and 30 ° dip. Then, f 1 = 1 2 π M B 1 c o s 45 ° I f 2 = 1 2 π M B 2 cos 30 ° I f 1 f 2 = B 1 c o s 45 ° B 2 c o s 30 ° ⇒ 30 2 40 2 = B 1 c o s 45 ° B 2 c o s 30 °   ⇒ B 1 B 2 = 900 × c o s 30 ° 1600 × c o s 45 ° ⇒ B 1 B 2 = 0.688 ≈ 0.7