(B) The velocity $v$ of a particle moving along a curved path can be resolved into radial $(v_r = dr/dt)$ and transverse $(v_{\theta} = r(d\theta/dt))

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(B) The velocity $v$ of a particle moving along a curved path can be resolved into radial $(v_r = dr/dt)$ and transverse $(v_{\theta} = r(d\theta/dt))$ velocity components.The angle $\alpha$ between the resultant velocity $v$ and the radial velocity $v_r$ is given by $\tan \alpha = v_{\theta} / v_r$.Substituting the expressions for $v_{\theta}$ and $v_r$:$\tan \alpha = \frac{r(d\theta/dt)}{dr/dt} = r \cdot \frac{d\theta}{dr} = \frac{r}{dr/d\theta}$Given that $dr/d\theta = r$,we have:$\tan \alpha = \frac{r}{r} = 1$Therefore,$\alpha = \tan^{-1}(1) = 45^{\circ}$.

Class 11 Physics 3-2.Motion in Plane Mix Examples-Motion in Plane

$A$ particle at a distance of $1 \ m$ from the origin starts moving,such that $dr/d\theta = r$,where $r$ and $\theta$ are polar coordinates. Then,the angle between the resultant velocity and the tangential velocity is

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A
$30^{\circ}$
B
$45^{\circ}$
C
$60^{\circ}$
D
dependent on where the particle is

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3-2.Motion in Plane

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Mix Examples-Motion in Plane

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$A$ particle at a distance of $1 \ m$ from the origin starts moving,such that $dr/d\theta = r$,where $r$ and $\theta$ are polar coordinates. Then,the angle between the resultant velocity and the tangential velocity is

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