Two objects of same volume and masses `m_1` and `m_2` are allowed to fall freely from the heights hi and h, respectively. Find the ratio of their time to reach earth's surface. Now, if (i) one of the objects is hollow and other is solid (ii) both of them are hollow. then what will be the effect on this ratio ?

Answer

`t_1/t_2=sqrt(h_(1)/h_(2))`, (i) No effect (ii) No effect

Explanation

The time t for a free falling object from height h to reach the earth.s surface is `t=sqrt((2h)/g`, because
`h=ut+1/2gt^(2), v=0`
`h=(0)t+1/2gt^(2)`
`t=sqrt((2h)/g)`
Now, for the object of mass `m_1, t_1=sqrt((2h_(1))/g` and for the object of mass `m_2. t_2=sqrt((2h_(2))/g`
`t_1/t_2=sqrt(h_1/h_2)`