A compass needle oscillates 20 times per minute at a place where the dip is 30 o and 30 times per minute where the dip is 60 o . The ratio of total magnetic field due to the earth at two places respectively is 4 x . The value of x is

Step-by-step solution

The formula for time period is given by T = 2 π I M B H ⇒ T = 2 π I M B cos θ Let θ 1 = 30 ° θ 2 = 60 ° The ratio of the time periods is, T 1 T 2 = 60 20 60 30 = B 2 cos 60 ° B 1 cos 30 ° = B 2 B 1 × 1 2 3 2 ⇒ B 1 B 2 = 4 243