Velocity <math><mrow><mrow><mo>(</mo><mrow><mi>υ</mi></mrow><mo>)</mo></mrow></mrow></math> and acceleration (a) in two system of units 1 and 2 are related as <math><mrow><msub><mrow><mi>υ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mfrac><mrow><mi>n</mi></mrow><mrow><msup><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><msub><mrow><mi>υ</mi></mrow><mrow><mn>1</mn></mrow></msub><mtext> </mtext><mtext> </mtext><mi>a</mi><mi>n</mi><mi>d</mi><mtext> </mtext><mtext> </mtext><msub><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mfrac><mrow><msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mrow><mi>m</mi><mi>n</mi></mrow></mfrac></mrow></math> respectively. Here m and n are constants. The relations for distance and time in two system respectively are:

Let, L1 & L2 one distance for system (1) & (2) respectivelyT1 & T2 are time for system (1) & (2) respectivelyGiven : v2 = nm2v1⇒(L2T2)=nm2(4T1) [?v2=L2T2,v1=L1T1]⇒L2L1=(nm2)[T2T1]−−(i)And a2 = a1mn⇒v2T2=v1T1mn⇒T1T2=v1v2(1mn) [?v1v2=m2n]⇒n2mT1=T2from (1)L2L1=nm2[n2m][?T2T1=n2m]⇒n3m3L1=L2

Velocity&nbsp;<math><mrow><mrow><mo>(</mo><mrow><mi>υ</mi></mrow><mo>)</mo></mrow></mrow></math>&nbsp;and acceleration (a) in two system of units 1 and 2 are related as&nbsp;<math><mrow><msub><mrow><mi>υ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mfrac><mrow><mi>n</mi></mrow><mrow><msup><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><msub><mrow><mi>υ</mi></mrow><mrow><mn>1</mn></mrow></msub><mtext> </mtext><mtext> </mtext><mi>a</mi><mi>n</mi><mi>d</mi><mtext> </mtext><mtext> </mtext><msub><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mfrac><mrow><msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mrow><mi>m</mi><mi>n</mi></mrow></mfrac></mrow></math>&nbsp;respectively. Here m and n are constants. The relations for distance and time in two system respectively are:

Ask & Answer Question

Physics Class 12th Units and Measurement physics ncert exemplar solutions class 12th chapter two

Velocity $(υ)$ and acceleration (a) in two system of units 1 and 2 are related as $υ_{2} = \frac{n}{m^{2}} υ_{1} a n d a_{2} = \frac{a_{1}}{m n}$ respectively. Here m and n are constants. The relations for distance and time in two system respectively are:

Option 1 -

$\frac{n^{3}}{m^{3}} L_{1} = L_{2} a n d \frac{n^{2}}{m} T_{1} = T_{2}$

Option 2 -

$L_{1} = \frac{n^{4}}{m^{2}} L_{2} a n d T_{1} = \frac{n^{2}}{m} T_{2}$

Option 3 -

$L_{1} = \frac{n^{2}}{m} L_{2} a n d T_{2} = \frac{n^{4}}{m^{2}} T_{2}$

Option 4 -

$\frac{n^{2}}{m} L_{1}, = L_{2} a n d \frac{n^{4}}{m^{2}} T_{1} = T_{2}$

2 Views | Posted 2 months ago

Asked by Shiksha User

1 Answer

Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Correct Option - 1

Detailed Solution:

Let, L₁ & L₂ one distance for system (1) & (2) respectively

T₁ & T₂ are time for system (1) & (2) respectively

Given : v2 = $\frac{n}{m^{2}} v_{1}$

$\Rightarrow (\frac{L_{2}}{T_{2}}) = \frac{n}{m_{2}} (\frac{4}{T_{1}})$ $[? v_{2} = \frac{L_{2}}{T_{2}}, v_{1} = \frac{L_{1}}{T_{1}}]$

$\Rightarrow \frac{L_{2}}{L_{1}} = (\frac{n}{m_{2}}) [\frac{T_{2}}{T_{1}}] - - (i)$

And a2 = $\frac{a_{1}}{m n} \Rightarrow \frac{v_{2}}{T_{2}} = \frac{v_{1}}{T_{1} m n}$

$\Rightarrow \frac{T_{1}}{T_{2}} = \frac{v_{1}}{v_{2}} (\frac{1}{m n})$ $[? \frac{v_{1}}{v_{2}} = \frac{m^{2}}{n}]$

$\Rightarrow \frac{n^{2}}{m} T_{1} = T_{2}$

from (1)

$\frac{L^{2}}{L_{1}} = \frac{n}{m^{2}} [\frac{n^{2}}{m}] [? \frac{T_{2}}{T_{1}} = \frac{n^{2}}{m}]$

$\Rightarrow \frac{n^{3}}{m^{3}} L_{1} = L_{2}$

0 Upvotes 0 Downvotes

Get authentic answers from experts, students and alumni that you won't find anywhere else

On Shiksha, get access to

65k Colleges
1.2k Exams
688k Reviews
1800k Answers

Community GuidelinesUser Points System

QuestionsDiscussionsTags

Velocity $(υ)$ and acceleration (a) in two system of units 1 and 2 are related as $υ_{2} = \frac{n}{m^{2}} υ_{1} a n d a_{2} = \frac{a_{1}}{m n}$ respectively. Here m and n are constants. The relations for distance and time in two system respectively are:

1 Answer

Learn more about...

Most viewed information

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question

Velocity (υ) and acceleration (a) in two system of units 1 and 2 are related as υ2=nm2υ1 and a2=a1mn respectively. Here m and n are constants. The relations for distance and time in two system respectively are:

1 Answer

Learn more about...

Most viewed information

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question

Velocity $(υ)$ and acceleration (a) in two system of units 1 and 2 are related as $υ_{2} = \frac{n}{m^{2}} υ_{1} a n d a_{2} = \frac{a_{1}}{m n}$ respectively. Here m and n are constants. The relations for distance and time in two system respectively are: