Saved Bookmarks
| 1. |
Consider a spongy block of mass m floating on a flowing river. The maximum mass of the block is related to the speed of the river flow v, acceleration due to gravity g and the density of the block rho such that m_(max)=kv^(x)g^(y)rhz^(z) (k is constant). The values of x, y and z should then respectively be (Mass of the spongy block is assumed to vary due to absorption of water by it) |
|
Answer» Solution :Since, the maximum mass of the block floating on river depends, speed of flow of the river =v, acceleration due to gravity =g and density of the block =`rho`, `m_(max)=KV^(x)g^(y)rho^(z)` WRITE the dimensional formula of the both side, we get, `[M^(1)L^(0)T^(0)]=[LT^(-1)]^(x)[LT^(-2)]^(y)[ML^(-3)]^(z)` `[M^(1)L^(0)T^(0)]=[M^(Z)L^(x+y-3z)T^(-x-2y)]` Compairing the dimensions of M, L and T on both sides, we get `z=1""....(i)` `x+y-3z=0""....(ii)` `-x-2y=0""......(iii)` `x+y-3xx1=0` [From Eq. (i) and (ii)] `x+y=3""....(iv)` From Eqs. (iii) and (iv), we get `-y=3rArry=-3` From Eq. (iv), we have `x-3=3` `impliesx=6` Hence, the value of x, y and z will be (6,-3,1). |
|