IIT JEE , AIEEE Forum - Physics , Mechanics - Assume that a tunnel is dug across the earth passing through it's centre.

sanjana_suri

find the time taken by a particle projected into the tunnel with speed

gR, to cover the length of the tunnel.

anchitsaini

T = 2

R / g or

=

g / R

v =

a ²- y ²

at pt A --

v =

gR

y = R

=

g / R

this gives

A =

2 R

using

y = A sin

t ₁

putting values we get --

t ₁ = 3

/ 4

cos the particle would start from mean position go to extreme and then come down to pt A ie its phase would be greater than

at pt B --

y = R

A =

2 R

now we put values in

y = A sin

t ₂

t ₂ = 5

/ 4

cos it has not reached extreme thus its phase is less than 3

/ 2

thus

( t ₂ - t ₁) =

/ 2

putting value of

we get

t = ( t ₂ - t ₁) =

/ 2 *

R / g

anchitsaini

figure

krishna.gopal

Perfect answer anchit. Well done