Question

Which of the following relation is not dimensionally correct? (K→kinetic energy, m→mass, v→speed, h→height, g→acceleration due to gravity) *​

Answer 1

Answer
h=
ρrg
2Scosθ
​

LHS=[L]
Surface tension =S=F/I=
L
MLT
−2

​
=[MT
−2
]
Density =ρM/V=[ML
−3
T
0
]
Radius =r=[L],g=[LT
−2
]
RHS=
ρrg
2Scosθ
​
=
[ML
−3
T
0
][L][LT
−2
]
[MT
−2
]
​
=[M
0
L
1
T
0
]=[L]
LHS=RHS
So, the relation is correct.

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