Suppose a tunnel is dug through the earth (assumed to be a homogeneous sphere) from one side to the other along a diameter. a body dropped into the tunnel takes

Suppose a tunnel is dug through the earth (assumed to be a homogeneous sphere) from one side to the other along a diameter. A body dropped into the tunnel takes a time f to reach the centre of the carth. if the accele ration due to gravity had remained unchanged, the body would have taken a time t2 to traverse this distance. What is the ratio t1 :2? Neglect friction offered to the motion. (In the first case, the motion of the body is simple harmonic with a period T-2 V Rlg where R is the radius of the earth and gis the acceleratien doe to gravty at its surface.)