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Q1.3: NCERT Physics - Part 1 UNITS AND MEASUREMENT 1.3 Solution: A calorie is a unit of heat (energy in transit) and it equals…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently assign the same sign to the conversion factors as the dimensional exponents (e.g., using $\alpha^1$ instead of $\alpha^{-1}$), failing to recognize that a larger new unit (larger $\alpha$) results in a smaller numerical value. Always apply the rule that the power of the conversion factor is the negative of the dimensional exponent: for $[M^a L^b T^c]$, the factor is $\alpha^{-a} \beta^{-b} \gamma^{-c}$.

A calorie is a unit of heat (energy in transit) and it equals about 4.2 J where 1 J = 1 kg m_ s__. Suppose we employ a system of units in which the unit of mass equals α\alpha kg, the unit of length equals β\beta m, the unit of time is γ\gamma s. Show that a calorie has a magnitude 4.2α−1β−2γ24.2 \alpha^{-1} \beta^{-2} \gamma^2 in terms of the new units.

Multiple Choice Options

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Step-by-Step Verified Solution

**Answer:**

1 calorie=4.2α−1β−2γ21 \text{ calorie} = 4.2 \alpha^{-1} \beta^{-2} \gamma^2 in the new units.

**Step-by-Step Explanation:**

Energy has dimensions [ML2T−2][M L^2 T^{-2}]. In the new system: - Unit of mass = α\alpha kg - Unit of length = β\beta m - Unit of time = γ\gamma s The conversion factor is:

1 calorie=4.2 kg m2 s−2=4.2(kgα kg)−1(mβ m)−2(sγ s)21 \text{ calorie} = 4.2 \text{ kg m}^2 \text{ s}^{-2} = 4.2 \left(\frac{\text{kg}}{\alpha \text{ kg}}\right)^{-1} \left(\frac{\text{m}}{\beta \text{ m}}\right)^{-2} \left(\frac{\text{s}}{\gamma \text{ s}}\right)^{2}
=4.2α−1β−2γ2 new units= 4.2 \alpha^{-1} \beta^{-2} \gamma^2 \text{ new units}

All Questions in this Chapter

Q1.1 Q1.2 Q1.3 Q1.4 Q1.5 Q1.6 Q1.7 Q1.8 Q1.9 Q1.10 Q1.11 Q1.12 Q1.13 Q1.14 Q1.15 Q1.16 Q1.17

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