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....

Question

Vishrant Vasavada · Answer

M -> V, d (density) and g

Let M (proportional to) V^ad^bg^c

Now Hence M = k V^ad^bg^cwhere k is constant of proportionality

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

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

M¹L⁰T⁰ = M^bL^{a - 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.

dip ak · Answer

M is directly proportional to v&circ;x M is directly proportional to d&circ;y M is directly proportional to g&circ;z 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

Saksham agarwal · Answer

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mahi · Answer

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

Kushagra Madhukar · Answer

Dear student,

Please find the attached answer to this question below.

Let M (proportional to) V^ad^bg^c

Now Hence M = k V^ad^bg^cwhere k is constant of proportionality

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

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

M¹L⁰T⁰ = M^bL^{a - 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.

Hope it helps.

Thanks and regards,

Kushagra

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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....

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....

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