A tunnel is made across the earth passing through its centre. A ball is dropped from a height h in the tunnel. The motion will be periodic with time period

$\mathrm{Inside} \mathrm{the} \mathrm{tunnel} \mathrm{the} \mathrm{motion} \mathrm{is} \mathrm{pure} \mathrm{shm} \mathrm{with} \mathrm{time} \mathrm{period} 2\mathrm{\pi }\sqrt{\frac{\mathrm{R}}{\mathrm{g}}} \mathrm{and} \mathrm{after} \mathrm{release} \mathrm{time} \mathrm{required} \mathrm{by} \mathrm{the} \mathrm{particle} \mathrm{to} \mathrm{strike} \mathrm{the} \mathrm{surface} \mathrm{of} \mathrm{earth} \mathrm{is} \sqrt{\frac{2\mathrm{h}}{\mathrm{g}}} .\mathrm{So} \mathrm{the} \mathrm{the} \mathrm{time} \mathrm{period} \mathrm{of} \mathrm{the} \mathrm{periodic} \mathrm{motion} ,\mathrm{T}={\mathrm{T}}_{\mathrm{shm}}+4\sqrt{\frac{2\mathrm{h}}{\mathrm{g}}}$