GATE-2018 (24) :Wyllie – Time average equation

CSIR - NET 2015

95. A 120 million year old rock situated close to the equator shows a remnant magnetic dip of tan^-1(-2/√3) . The approximate drift rate of the land mass is

 

A) 1.25 cm/year

 

B) 2.75 cm/year

 

C) 3.70 cm/year

 

D) 5.00 cm/year

 

Solution:

 

Using tan I= 2tanΦ, using this equation to reconstruct the history of paleo-latitudes.

 

Inclination (I) : distance to the north pole (dip)

 

Given data

 

Time = 120 * 10⁶ years

 

tanI = 2 tan Φ ---------------(1)

 

I = tan^-1 (2 tan Φ) -------------------(2)

 

From given problem

 

I= tan^-1(-2/√3) -----------(3)

 

Compare eq (3) and eq (2)

 

Therefore,

 

2 tan Φ = (-2/√3)

 

tanΦ = (-1/√3)

 

Φ= tan^-1 (-0.577)

 

Φ= -30⁰ N or 30⁰S

 

Then approximate drift rate of land mass

 

Φ= 30⁰ S

 

     = 30 * 110 km (1⁰= 110 km)

 

     = 3300 km

 

      = 3300000 m

     =330000000 cm

 

Therefore,

 

$Drift rate (V) = \frac{Distance}{time}$

 

$Drift rate (V) = \frac{330000000}{ 120000000}$

             

 Drift rate (V) = 2.75 cm/yr