A calorie is a unit of heat energy and its value is 4.18 J where 1 J = 1 kg m2 s-2. Suppose we use a new system of units in which unit of mass equals α kg, the unit of length equals β m and the unit of the time is γ sec. Then the value of a calorie in the new system of units is

Question

A calorie is a unit of heat energy and its value is 4.18 J where 1 J = 1 kg m2 s-2. Suppose we use a new system of units in which unit of mass equals α kg, the unit of length equals β m and the unit of the time is &gamma; sec. Then the value of a calorie in the new system of units is (A) 4.18 (&gamma;2/αβ2) (B) 4.18 (αβ2/&gamma;2) (C) 4.18 (&gamma;2/α) (D) 4.18 (β2/α&gamma;2)

Tardigrade Admin · Accepted Answer

1 J=(1 kg)(1 m)2(1 sec)-2 1x=(α kg)(β m)2(&gamma; sec)-2 ∴ (1 J/1x)=((1/α))((1/β))2(&gamma;)2=(&gamma;2/αβ2) ∴ 1 J=(&gamma;2/αβ2)x or 1 cal=4.18 (&gamma;2/αβ2)

$4.18 \frac{γ ^{2}}{α β ^{2}}$

$4.18 \frac{α β ^{2}}{γ ^{2}}$

$4.18 \frac{γ ^{2}}{α}$

$4.18 \frac{β ^{2}}{α γ ^{2}}$

$1 J = (1 k g) (1 m)^{2} (1 sec)^{- 2}$
$1 x = (α k g) (β m)^{2} (γ sec)^{- 2}$
$∴ \frac{1 J}{1 x} = (\frac{1}{α}) (\frac{1}{β})^{2} (γ)^{2} = \frac{γ ^{2}}{α β ^{2}}$
$∴ 1 J = \frac{γ ^{2}}{α β ^{2}} x$ or $1 c a l = 4.18 \frac{γ ^{2}}{α β ^{2}}$

Q. A calorie is a unit of heat energy and its value is 4.18J where 1J=1kgm2s−2. Suppose we use a new system of units in which unit of mass equals αkg, the unit of length equals βm and the unit of the time is γsec. Then the value of a calorie in the new system of units is

4.18αβ2γ2​

4.18γ2αβ2​

4.18αγ2​

4.18αγ2β2​

1J=(1kg)(1m)2(1sec)−2 1x=(αkg)(βm)2(γsec)−2 ∴1x1J​=(α1​)(β1​)2(γ)2=αβ2γ2​ ∴1J=αβ2γ2​x or 1cal=4.18αβ2γ2​

$4.18 \frac{γ ^{2}}{α β ^{2}}$

$4.18 \frac{α β ^{2}}{γ ^{2}}$

$4.18 \frac{γ ^{2}}{α}$

$4.18 \frac{β ^{2}}{α γ ^{2}}$

$1 J = (1 k g) (1 m)^{2} (1 sec)^{- 2}$
$1 x = (α k g) (β m)^{2} (γ sec)^{- 2}$
$∴ \frac{1 J}{1 x} = (\frac{1}{α}) (\frac{1}{β})^{2} (γ)^{2} = \frac{γ ^{2}}{α β ^{2}}$
$∴ 1 J = \frac{γ ^{2}}{α β ^{2}} x$ or $1 c a l = 4.18 \frac{γ ^{2}}{α β ^{2}}$