Question

Q7. A calorie is a unit of heat and it equals to 4.2 joule. We employ a system of units in which the unit of mass equals 4 kg, unit of length equals 2 m and unit of time equals 2 second. Find the value of 1 calorie in this new system of units.​

Answer 1

$8.4J$

Explanation:

$Given, \: \: 1cal = 4.2J \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 4.2 \: kg {m}^{2} {s}^{ - 2} \\ A/Q, \: \: taking \: \: m=4kg, \: l=2m \: \: and \: \: t=2s \\ in \: \: the \: \: new \: \: system, \\ then, \: \: \: 1 \: cal = 4.2 \times 2 \: kg \times (2m)^{2} \times (2s)^{ - 2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 4.2 \times 2 \: kg \times 4 \: {m}^{2} \times \frac{1}{4} {s}^{ - 2} \\ = 8.4 \: kg {m}^{2} {s}^{ - 2} \\ = \boxed{ 8.4J}$