Two objects of massses `m_(1)` and `m_(2)` having the same size are dropped simultaneously from hights `h_(1) and h_(2)` respectively. Find out the ratio of time they would take in reaching the ground. Will this ratio remain the same if (i)one of the objects is hollow and the other one is solid and (ii)both of them are hollow, size remaining the same in each case. give reason.

Explanation

From second equation of motion, `h=ut+(1)/(2)"gt"^(2)`" "[for I objectu=0]
`So," "h=(1)/(2)"gt"^(2)`
where, h = Displacement, u = Initial velocity, t = Time andg = Acceleration due to gravity
`rArr" ""gt"^(2)=2hrArrt^(2)=(2h)/(g)`
`i.g.," "t=sqrt((2h)/(g)`
`:."Time taken by first object of mass",m_(1)`
`" "t_(1)=sqrt((2h_(1))/(g))" "` [for II object u = 0]
Similary, time taken by object of mass `m_(2)`
`" "t_(2)sqrt((2h_(2))/(g))rArr(t_(1))/(t_(2))=sqrt((h_(1))/(h_(2))`
(i) Acceleration due to gravity is independent of mass of falling body. So, the ratio remains the same.
(ii) If bodies are hollow, then also ratio remains the same `i.g., t_(1):t_(2)=sqrt(h_(1)):sqrt(h_(2))`