Two objects of masses `m_(1)` and `m_(2)` having the same size are dropped simultaneously from heights `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

As the two masses are dropped,`u=0,a=g` (which does not depend upon mass)
From `s =ut+ (1)/(2) at^(2)`
`h_(1) = 0 +(1)/(2) g t_(1)^(2)` and `h_(2) = 0 +(1)/(2) g t_(2)^(2)`
`:. (h_(1))/(h_(2))=(t_(1)/t_(2))^(2) or (t_(1))/(t_(2))=sqrt(h_(1)/(h_(2)))`
This ratio of time shall remain the same if
(i)one of the objects is hollow and the other one is solid-as the ratio is independent of masses. (ii) both the objects are hollow, as acc. due is gravity (g) does not depent upon mass and also whether the body is hollow/solid.
As size remains the same in each case, there is no effect of resistance due to air in the two cases.