Q94 / 180 · NEET 2015 (Phase 1) · Physics

If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be___(For surface tension, Force=Surface tension×length)

  • A
    E V-2 T-1
  • B
    E V-1 T-2
  • Correct answer
    C
    E V-2 T-2
  • D
    E-2 V-1 T-3

Solution

Dimensional formula of surface tension, S=M1L0T-2
Dimensional formula of energy, E=M1L2T-2
Dimensional formula of velocity, V=M0L1T-1

By applying dimensional analysis,
S=EaVbTc
M1L0T-2=M1L2T-2aM0L1T-1bTc
M1L0T-2=MaL2a+bT-2a-b+c

On comparing,
a=1
2a+b=0⇒b= -2
-2a-b+c=-2⇒c= -2
∴S=E1V-2T-2

Hence, the correct answer is option: 'C'.

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