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NEET 1992 (AIPMT) · Units & Dimensions

Units & Dimensions question from NEET 1992 (AIPMT)

Q113NEET 1992 · AIPMTMedium

Units & Dimensions

PP represents radiation pressure, cc represents speed of light and SS represents radiation energy striking per unit area per sec. The non zero integers x,y,zx, y, z such that PxSyczP^{x}S^{y}c^{z} is dimensionless are

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Answer: (c)

  1. [P]=[ML−1T−2][P] = [\mathrm{ML^{-1}T^{-2}}], [S]=energyarea⋅time=[MT−3][S] = \dfrac{\text{energy}}{\text{area}\cdot\text{time}} = [\mathrm{MT^{-3}}], [c]=[LT−1][c] = [\mathrm{LT^{-1}}].
  2. Since P=S/cP = S/c, the ratio PcS\dfrac{Pc}{S} is dimensionless.
  3. Check: P1S−1c1=[ML−1T−2][M−1T3][LT−1]=[M0L0T0]P^1S^{-1}c^1 = [\mathrm{ML^{-1}T^{-2}}][\mathrm{M^{-1}T^{3}}][\mathrm{LT^{-1}}] = [\mathrm{M^0L^0T^0}].
  4. So the answer is (c) x=1, y=−1, z=1x = 1,\ y = -1,\ z = 1.
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