(Solved): Problem 7: \( 3+2+1 \) Points Assume that there is a straight tunnel through the earth connecting t ...

Problem 7: \( 3+2+1 \) Points Assume that there is a straight tunnel through the earth connecting the North Pole with the South Pole. An object with a mass of \( m=10^{3} \mathrm{~kg} \) is released at the North Pole and falls towards the earth's centre. a. What is the time needed for the object to reach the South Pole? b. What is its velocity at the earths centre? c. Assume that at the centre of the earth the object receives an impulse of \( 10^{4} \mathrm{Ns} \) in the direction of its velocity (i.e. the linear momentum of the object is instantly increased by \( 10^{4} \mathrm{Ns} \) ). What is the velocity of the object at the South Pole? \( 2 \mid 3 \) Hint: Assume that the earth is a sphere with a homogenous density. The mass is \( m_{E}=5.97 \cdot 10^{24} \mathrm{~kg} \), the radius is \( 6378 \mathrm{~km} \). The gravitational constant is \( G=6.67 \cdot 10^{-11} \mathrm{~m}^{3} \mathrm{~kg}^{-1} \mathrm{~s}^{-2} \).