Question

Two objects of masses m_{1 a}nd m₂ have the same size are dropped simultaneously from heights h₁ and h₂ 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.

Answer 1

For the object of mass m1 dropped from height h₁, u = 0 a = g s = h₁

Using s = `"ut" + 1/2 "at"^2`, we get h1 = `0 + 1/2 "gt"_1^2` 

or `"t"_1 = sqrt((2"h"_1)/"g")`

Similarly, for the object of mass m₂ dropped from height h₂,

`"t"_2 = sqrt((2"h"_2)/"g")`

∴ `("t"_1)/("t"_2) = sqrt((2"h"_1)/"g") xx sqrt("g"/(2"h"_1)) = sqrt("h"_1/"h"_2)`

Yes, the ratio remains the same in both the cases as this ratio is independent of mass and size of the objects.