Question

Convert the following using dimensions:
-- Value of 120 Joule per minute on a new system of units having base units as 20cm, 250g, 0.5minute.

Units and Measurements, Physics.
Class XIth.

Answer 1

Answer:

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Answer 2

EXPLANATION :-

We know that,

1 Joule = 1 kg m/s²

• (where, s = second that remains same in all systems.)

[We need to convert it and find its value in new system in terms of gm, cm, min.]

$\red{ \sf \rightarrow \: n _{1}u _{1} = n _{2}u _{2}}$

$\red{ \sf \rightarrow \: 120 \: \: \frac{ \frac{kg \: m}{ {s}^{2} } }{min} = n _{2} \: \: \frac{ \frac{250g \: 20cm}{ {s}^{2} } }{0.5min} }$

$\red{ \sf \rightarrow \: 120 \: \: \frac{kg \: m}{ \cancel{{s}^{2}} \: min} = n _{2} \: \: \frac{250g \: 20cm}{ \cancel{{s}^{2}} \: min} }$

$\red{ \sf \rightarrow \: 120 \: \: ({10}^{3} )g \: ( {10}^{2})cm \: {(min)}^{ - 1} = n _{2} \: \: {(250)g \: (20)cm} \: {(0.5)min {}^{ - 1} } } \\ \\ \red{ \sf \rightarrow \: 120 \: \: { \huge{(}} \frac{{10}^{3} { \cancel{g}}}{250{ \cancel{g}}} { \huge{)}} \: { \huge{( }} \frac{{10}^{2}{ \cancel{cm}}}{20{ \cancel{cm}}} { \huge{)}} \: { { \huge{(}} \frac{{ \cancel{min}}}{0.5{ \cancel{min}}} { \huge{)}}}^{ - 1} = n _{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

${ \red{ \sf{ \rightarrow{ \: 120 \times \frac{ {10}^{3} }{250} \times \frac{ {10}^{2} }{20} \times { \huge{(}} \frac{1}{0.5} { \huge{)}} {}^{ - 1} = n _{2} }}}} \\ \\ { \red{ \sf{ \rightarrow{ \: 120 \times \frac{1000}{250} \times \frac{100}{20} \times 0.5 = n _{2} }}}} \: \: \: \: \: \: \: \: \: \\ \\ { \red{ \sf{ \rightarrow{ \: n _{2} = 120 \times \frac{ \cancel{100} {}^{ \cancel{20} {}^{10} } \cancel0}{\cancel{25} \cancel0 _{ \cancel5} } \times \frac{1 \cancel{0} \cancel{0}}{ \cancel2 \cancel0} \times \frac{\cancel5}{1 \cancel0} }}}} \: \: \: \\ \\ { \boxed { \red{ \sf{ \rightarrow{ \: n _{2} = 1200}}}}}$

I had taken seconds on the right side as well as you know second will be cancelled since it is same in all systems.