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  • Velocity  and acceleration <img alt="\mathrm{\text { (a) }}" src="/latex-image/?%5Cmathrm%7B%5Ctext%20%7B%20%28a%

Velocity \mathrm{(v)} and acceleration \mathrm{\text { (a) }} in two systems of units 1 and 2 are related as \mathrm{v_{2}=\frac{n}{m^{2}} v_{1}} and \mathrm{\mathrm{a}_{2}=\frac{\mathrm{a}_{1}}{\mathrm{mn}}} respectively. Here m and n are constants. The relations for distance and time in two systems respectively are: 

Option: 1

\mathrm{\frac{\mathrm{n}^{3}}{\mathrm{~m}^{3}} \mathrm{~L}_{1}=\mathrm{L}_{2} \text { and } \frac{\mathrm{n}^{2}}{\mathrm{~m}} \mathrm{~T}_{1}=\mathrm{T}_{2}}


Option: 2

\mathrm{L}_{1}=\frac{\mathrm{n}^{4}}{\mathrm{~m}^{2}} \mathrm{~L}_{2} \text { and } \mathrm{T}_{1}=\frac{\mathrm{n}^{2}}{\mathrm{~m}} \mathrm{~T}_{2}


Option: 3

\mathrm{L}_{1}=\frac{\mathrm{n}^{2}}{\mathrm{~m}} \mathrm{~L}_{2} \text { and } \mathrm{T}_{1}=\frac{\mathrm{n}^{4}}{\mathrm{~m}^{2}} \mathrm{~T}_{2}


Option: 4

\frac{\mathrm{n}^{2}}{\mathrm{~m}} \mathrm{~L}_{1}=\mathrm{L}_{2} \text { and } \frac{\mathrm{n}^{4}}{\mathrm{~m}^{2}} \mathrm{~T}_{1}=\mathrm{T}_{2}


Answers (1)

best_answer

Dimension of length \mathrm{(L)}

\mathrm{L=\frac{v^{2}}{a}}

\mathrm{\frac{v_{2}^{2}}{a_{2}}=\frac{\left [ \frac{n}{m^{2}}v_1 \right ]^{2}}{\left [ \frac{a_{1}}{mn} \right ]}}

\mathrm{\frac{\left[v_{2}\right]^{2}}{\left[a_{2}\right]}=\frac{n^{3}}{m^{3}} \frac{\left[v_{1}\right]^{2}}{\left[a_{1}\right]}}

Or

\mathrm{\left[L_{2}\right]=\left[\frac{n^{3}}{m^{3}}\right]\left[L_{1}\right]}

Similarly

\mathrm{[T]=\left[\frac{V}{a}\right]}

\mathrm{\left[T_{2}\right]=\frac{n^{2}}{m}\left[T_{1}\right]}

Hence, the correct answer is (1)

Posted by

Pankaj Sanodiya

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