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 such that m_ =k v^x g^y ^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)

Step-by-step 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 = , m_ =k v^x g^y ^z Compairing the dimensions of M , L and T on both sides, we get z=1 aligned x+y-3 z & =0 -x-2 y & =0 x+y-3 1 & =0[ [From Eq. (i) and (ii)] x+y & =3 aligned From Eqs. (iii) and (iv), we get -y=3 y=-3 From Eq. (iv), we have aligned & & x-3 & =3 & & x & =6 aligned Hence, the value of x, y and z will be (6,-3,1) .