Physics · Units, Dimensions & Error Analysis

JEE Advanced 2020 — Paper 1 — Question 8

Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity. In one such system, dimensions of different quantities are given in terms of a quantity X as follows: $[$ position $]=\left[\mathrm{X}^{\alpha}\right] ;[$ Speed $]=\left[\mathrm{X}^{\beta}\right]$ ; [acceleration $]=\left[\mathrm{X}^{\mathrm{p}}\right]$ ; [Linear momentum $]=\left[\mathrm{X}^{q}\right]$ ; [force] $=\left[X^{\prime}\right]$ . Then

Option A:
$\alpha+p=2 \beta$
Correct
Option B:
$p+q-r=\beta$
Correct
Option C:
$p-q+r=\alpha$
Option D:
$p+q+r=\beta$

Answer: A, B

Step-by-step solution

$r=x^{\alpha}$

$v=x^{\beta}$

$\mathrm{a}=\mathrm{x}^{\mathrm{P}}$

$P=x^{q}$

$\mathrm{F}=\mathrm{x}^{\mathrm{r}}$

(A) $\mathrm{ra} \rightarrow\left[\mathrm{X}^{\alpha+\mathrm{P}}\right]$

$\left[\frac{\text { Energy }}{\text { mass }}\right]=[2 \beta]$

(B) $\left[\frac{\mathrm{aP}}{\mathrm{F}}\right]=[\mathrm{at}]=[\mathrm{v}]=\beta$

$P+q-r=\beta$

Answer key and solution verified before publishing.

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Exam: JEE Advanced 2020
Paper: Paper 1
Subject: Physics
Chapter: Units, Dimensions & Error Analysis
Topic: Units and Dimensions Analysis