A particle is dropped down in a deep hole which extends to the centre of the earth. Calculate the velocity at a depth of one km from the surface of this carth ? Assume that g= 10 m//s^2and radius of the earth = 6400 km.

A particle is dropped down in a deep hole which extends to the centre

1.	A particle is dropped down in a deep hole which extends to the centre of the earth. Calculate the velocity at a depth of one km from the surface of this carth ? Assume that g= 10 m//s^2and radius of the earth = 6400 km.
Answer» Solution :`T=2pisqrt(R//g)=2pisqrt(6.4xx10^(6)//10)=5024` SECOND `, omega =2pi//T=0.00215" rad s"^(-1)` Velocity `v=omegasqrt(a^2-y^2)=0.00215sqrt((6.4xx10^6)-(6.399xx10^6)^2)=1.44xx10^(12)MS^(-1)`