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3-2.Motion in Plane
medium
A particle is rotating in a circle of radius $1\,m$ with constant speed $4\,m / s$. In time $1\,s$, match the following (in $SI$ units) columns.
| Colum $I$ | Colum $II$ |
| $(A)$ Displacement | $(p)$ $8 \sin 2$ |
| $(B)$ Distance | $(q)$ $4$ |
| $(C)$ Average velocity | $(r)$ $2 \sin 2$ |
| $(D)$ Average acceleration | $(s)$ $4 \sin 2$ |
A$( A \rightarrow r , B \rightarrow q , C \rightarrow r , D \rightarrow p )$
B$( A \rightarrow p , B \rightarrow q , C \rightarrow r , D \rightarrow p )$
C$( A \rightarrow r , B \rightarrow s , C \rightarrow r , D \rightarrow p )$
D$( A \rightarrow p , B \rightarrow q , C \rightarrow r , D \rightarrow s)$
Solution
(a)$\omega=\frac{v}{R}=\frac{4}{1}=4\,rad / s$
$\theta=\omega t=4\,rad$
$\text { Displacement }=A B=2 R \sin \frac{\theta}{2}$
$=2 \sin 2 \text { unit }$
$\text { Distance }=v t=4 \text { unit }$
$\text { Average velocity }=\frac{\text { Displacement }}{\text { Time }}=2 \sin 2 \text { unit }$
$\text { And average acceleration }=\frac{|\Delta v|}{\Delta t}$
From subtraction of vectors, we can find that change in velocity from $A$ and $B$ is $2 v \sin \frac{\theta}{2}=8 \sin 2$ unit
$\therefore \quad \text { Average acceleration } =\frac{8 \sin 2}{1}$
$=8 \sin 2 \text { unit }$
Standard 11
Physics
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