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

Q: 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 $]=\left[X^\alpha\right] ;[$ speed $]=\left[X^\beta\right]$; [acceleration $]=\left[X^{ p }\right]$; [linear momentum $]=\left[X^{ q }\right]$; [force $]=\left[X^{ I }\right]$. Then - $(A)$ $\alpha+p=2 \beta$ $(B)$ $p+q-r=\beta$ $(C)$ $p-q+r=\alpha$ $(D)$ $p+q+r=\beta$

a Given $L =x^\alpha$ $. . . . . . (1)$ $LT ^{-1}=x^\beta$ $. . . . . . (2)$ $LT ^{-2}=x^{ p }$ $. . . . . . (3)$ $MLT ^{-1}=x^q$ $. . . . . . (4)$ $MLT ^{-2}=x^{ I }V$ $. . . . . . (5)$ $\quad \frac{(1)}{(2)} \Rightarrow T =x^{\alpha-\beta}$ From $(3)$ $\frac{ x ^\alpha}{ x ^{2(\alpha-\beta)}}= x ^{ p }$ $\Rightarrow \alpha+ p =2 \beta$ From $(4)$ $M=x^{q-\beta}$ From $(5)$ $\Rightarrow x ^{ q }= x ^{ T } x ^{\alpha-\beta}$ $\Rightarrow \alpha+ r - q =\beta$ Replacing value ' $\alpha$ ' in equation $(6)$ from $(A)$ $2 \beta- p + r - q =\beta$ $\Rightarrow p + q - r =\beta$ Replacing value of ' $\beta$ ' in equation $(6)$ from $(A)$ $2 \alpha+2 r-2 q=\alpha+p$ $\alpha=p+2 q-2 r$

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

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 $]=\left[X^\alpha\right] ;[$ speed $]=\left[X^\beta\right]$; [acceleration $]=\left[X^{ p }\right]$; [linear momentum $]=\left[X^{ q }\right]$; [force $]=\left[X^{ I }\right]$. Then -

$(A)$ $\alpha+p=2 \beta$

$(B)$ $p+q-r=\beta$

$(C)$ $p-q+r=\alpha$

$(D)$ $p+q+r=\beta$

A$A,B$
B$A,C$
C$A,D$
D$B,C$

IIT 2020, Advanced

STD 11 Science
JEE
STD 11 - 1. units,dimensions and measurement
Physics

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