Question

The earth has a radius of 6400 km. The inner core of
1000 km radius is solid. Outside it, there is a region
from 1000 km to a radius of 3500 km which is in
molten state. Then again from 3500 km to 6400 km,
the earth is solid. Only longitudinal (P) waves can
travel inside a liquid. Assume that the P wave has
a speed of 8 km s' in solid parts and of 5 km s
in liquid parts of the earth. An earthquake occurs at
some place close to the surface of the earth. Find the
time after which it will be recorded in a seismometer
at a diametrically opposite point on the earth if wave
travels along diameter.
A. 41.25 min
B. 32.91 min
16.45 min
D. 14.06 min​

Answer 1

Answer:

sorry i dont know the answer because it is too long to understand

Answer 2

The time taken is 32.91 min.

(B) is correct option

Explanation:

Given that,

Radius of earth = 6400 km

Radius of inner core = 1000 km

Speed in solid= 8 km/s

Speed in liquid = 5 km/s  

According to figure,

OZ=OZ'=1000 km

OY=OY'=3500 km

OX=OX'=6400 km

The wave travels along the diameter of earth starting from X, is has to travel the following distances to get recorded in a seismometer at X′

We need to calculate the distance for solid

Using formula for distance

$d=X'Y'+Z'O+OZ+YX$

$d=(OX'-OY')+Z'O+OZ+(OX-OY)$

Put the value into the formula

$d=(6400-3500)+1000+1000+(6400-3500)$

$d=7800\ Km$

We need to calculate the distance for liquid

Using formula for distance

$d'=ZY+Z'Y'$

$d'=OY-OZ+OY'-OZ'$

Put the value into the formula

$d'=(3500-1000)+(3500-1000)$

$d'=5000\ km$

We need to calculate the time taken

Using formula of time

$t=\dfrac{d}{v}+\dfrac{d'}{v'}$

Where, d = distance in solid

d'= distance in liquid

v = velocity of wave in solid

v' =velocity of wave in liquid

Put the value into the formula

$t=\dfrac{7800}{8}+\dfrac{5000}{5}$

$t=1975\ sec$

$t=\dfrac{1975}{60}\ min$

$t=32.91\ min$

Hence, The time taken is 32.91 min.

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Topic : Time taken

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