Question

convert 10 joule to ergs in dimensional analysis

Answer 1

$\underline{\bold{Solution:-}}$

First of all we have to write the dimensional formula of joule.

Dimensional formula of joule is ${M}^{1} {L}^{2} {T}^{ - 2}$

n1 = 1

M1 = 1 kg

M2 = 1 gm

L1 = 1 m

L2 = 1 cm

T1 = 1 sec

T2 = 1 sec

Let n1 be the number of joule and n2 be the number of erg.

n1 [M₁¹L₁²T₁⁻²] = n2 [M₂¹L₂²T₂⁻²]

On dividing both sides by [M₂¹L₂²T₂⁻²].

n1 [M₁¹L₁²T₁⁻²] / [M₂¹L₂²T₂⁻²] = n2

n2 = n1 [M₁¹L₁²T₁⁻²] / [M₂¹L₂²T₂⁻²]

On Separating same term

$n_{2} \: = \: n_{1} \times { [\frac{M_{1} }{M_{2} }]}^{1} \times { [\frac{L_{1} }{L_{2} }]}^{2} \times { [\frac{T_{1} }{T_{2} }]}^{ - 2} \\ \\on \: putting \: there \: values \\ \\ n_{2} \: = \: n_{1} \times { [\frac{1 \: kg}{1 \: gm} ]}^{1} \times {[ \frac{1 \: m}{1 \: cm} ]}^{2} \times { [\frac{1 \: sec}{1 \: sec} ]}^{ - 2} \\ \\ n_{2} \: = \: n_{1} \times {[ \frac{1000 \: gm}{1 \: gm}]}^{1} \times { [\frac{100 \: cm}{1 \: cm} ]}^{2} \times { 1 }^{ - 2} \\ \\ n_{2} \: = \: 1 \times {10}^{7} \\ \\ n_{2} \: = \: {10}^{7} \\ \\ so \: 1 \: joule \: = \: {10}^{7} \: erg$

Answer 2

The answer is 10⁸ erg.

Given,

10 joules

To Find,

Convert 10 joules to erg using dimensional analysis.

Solution,

1 joule = M¹ L² T⁻²

10 joules = ____ erg

n₁ u₁ = _n₂_ u₂

n₂ = $n1[\frac{M1}{M2}]^a[\frac{L1}{L2}]^b[\frac{T1}{T2}]^c$

n₂ = $10[\frac{1kg}{1g}]^1 [\frac{1m}{1cm}]^2 [\frac{1s}{1s}]^-^2$

n₂ = (10)(10³)(10²)²

n₂ = 10⁸ erg

Hence, the answer is 10⁸ erg.