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saurabh Grade:
        

assuming that mass M of the largest stone that can be moved by a flowing river depends 'v' velocity,densityof water and g acc. due to gravity.show that M varies with 6th power of velocity of flow....

7 years ago

Answers : (2)

Vishrant Vasavada
23 Points
										

M -> V, d (density) and g


 


    Let M (proportional to) Vadbgc


Now Hence M = k Vadbgwhere k is constant of proportionality


[M] = [V]a[d]b[g]c


M1L0T0 = (L1T-1)a(M1L-3)b(L1T-2)c


M1L0T0 = Mb La - 3b + c  T-a - 2c


Comparing the powers,


 


b = 1


a - 3b + c = 0


Hence,


 


a - 3(1) + c = 0


a + c = 3  ...........1


-a - 2c = 0 ............2


 


Solving equations 1 and 2,


a + c =  3


-a - 2c = 0


---------------


     -c = 3


Hence, c = - 3.


Substituting c = -3 in equation 1, we get a = 6.


Thus, M = k V6dg


hence, it can be said that M varies with 6th power of velocity.


Hint: In any type of problems of dimensional analysis where it is given that This quantity depends on so and so... solve by this method always. It would be easier.


 

7 years ago
dip ak
16 Points
										

M is directly proportional to vˆx


M is directly proportional to dˆy


M is directly proportional to gˆz


m=k*v^x*d^y*g^z


m=(l*t^-1)^x*(m*l)^y*(lt^-2)^z


y=1


-x-2*z=0


z=-x/2


x-3*y-x/2=0


x=6


m=v^6


-3

6 years ago
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