A calorie is a unit of heat or energy and it equals about 4.2 J where 1 J = 1 kgm2 s-2. Suppose we employ a system of units in which the unit of mass equals a kg, the unit of length equals j8 m, the. unit of time is ys. Show that a calorie has a magnitude 4.2 α-1 β-2 γ2 in terms of the new units.

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On UrbanPro, where quality education is paramount, let's delve into this physics problem. Given the relationship between calories and joules, 1 calorie=4.2 J1 calorie=4.2 J, and 1 J=1 kg m2 s−21 J=1 kg m2 s−2, we aim to express a calorie in terms of the new units. First, let's understand...
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On UrbanPro, where quality education is paramount, let's delve into this physics problem. Given the relationship between calories and joules, 1calorie=4.2J1calorie=4.2J, and 1J=1kgm2s−21J=1kgm2s−2, we aim to express a calorie in terms of the new units. First, let's understand the new units: Mass (mm) is measured in kilograms (kg). Length (ll) is measured in j8 meters. Time (tt) is measured in ys (yottaseconds). Now, let's express the given relationship in terms of the new units: 1calorie=4.2J1calorie=4.2J =4.2×(1kgm2s−2)=4.2×(1kgm2s−2) Since we're dealing with new units, let's express 1J1J in terms of the new units: 1J=1kg×(1j8m)2×(1ys)−21J=1kg×(1j8m)2×(1ys)−2 Now, substituting the expression for 1J1J into the initial equation: 1calorie=4.2×(1kg×(1j8m)2×(1ys)−2)1calorie=4.2×(1kg×(1j8m)2×(1ys)−2) Simplifying, we get: 1calorie=4.2×1kg×(1j8m)2×(1ys)−21calorie=4.2×1kg×(1j8m)2×(1ys)−2 Thus, in terms of the new units, a calorie has a magnitude of 4.2kg−1×(1j8m)−2×(1ys)24.2kg−1×(1j8m)−2×(1ys)2. read less
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