If energy E, speed v and time T are the fundamental units, the dimensional formula of surface tension is EˣvʸTᶻ. Find x − y + z.
Physics · Mixed Chapter
JEE Mains

Question

If energy E, speed v and time T are the fundamental units, the dimensional formula of surface tension is EˣvʸTᶻ. Find x − y + z.

G1 Physics · Accepted Answer

Step 1 — Fundamental dimensions: [E] = ML²T⁻²; [v] = LT⁻¹; [T] = T. Step 2 — Surface tension equals force per unit length, so [S] = MT⁻². Step 3 — Assume [S] = EˣvʸTᶻ. Matching powers gives MˣL⁽²ˣ⁺ʸ⁾T⁽⁻²ˣ⁻ʸ⁺ᶻ⁾ = M¹L⁰T⁻². Step 4 — Mass powers: x = 1. Length powers: 2x + y = 0, so y = −2. Step 5 — Time powers: −2x − y + z = −2. Insert x = 1 and y = −2: −2 + 2 + z = −2, so z = −2. Step 6 — Required x − y + z = 1 − (−2) − 2 = 1. Answer: 1.