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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....

10 years ago

Answers : (4)

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.

 

10 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

9 years ago
Saksham agarwal
15 Points
							
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one year ago
mahi
13 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

2 months ago
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