The kinetic energy (k) of the largest stone that can be moved by flowing river depends upon the velocity v of water , density d of water and acceleration due to gravity g.then
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Answer:
Let V is the volume, d is the density and g
Let M∝V
a
d
b
g
c
Now,
M=kV
a
d
b
g
c
[M]=[V]
2
[d]
b
[g]
c
M
1
L
0
T
0
=(L
1
T
−1
)
a
(M
1
L
−3
)
b
(L
1
T
−2
)
c
M
1
L
0
T
0
=M
b
L
a−3b+c
T
−a−2c
Comparing the powers
b=1
a−3b+c=0
a−3(1)+c=0
a+c=3......(1)
−a−2c=0....(2)
Solving (1) and (2)
a+c=3
−a−2c=0
--------------------
−c=3
Substitute c=−3 in equation (1)
We get a=6
Thus
M=kV
6
dg
Hence, it can be said that M varies with 6th power of velocity.
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