A stone tied to 180 cm long string at its end is making 28 revolutions in horizontal circle in every

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3-2.Motion in Plane

easy

A stone tied to $180 cm$ long string at its end is making 28 revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is $\frac{1936}{ x }\,ms ^{-2}$. The value of $x.........\left(\text { Take } \pi=\frac{22}{7}\right)$

A$124$

B$123$

C$125$

D$122$

(JEE MAIN-2023)

Solution

$a=\omega^2 R=\left(\frac{28 \times 2 \pi}{60}\right)^2 \times 1.8$
$=\left(\frac{56}{60} \times \frac{22}{7}\right)^2 \times 1.8$
$=\frac{(44)^2}{225} \times 1.8$
$=\frac{1936 \times 1.8}{225}$
$x=125$

Standard 11

Physics

A stone ties to the end of a string $1\,m$ long is whirled in a horizontal circle with a constant speed. If the stone makes $22$ revolution in $44$ seconds, what is the magnitude and direction of acceleration of the stone

medium

(AIIMS-2014)

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Centripetal acceleration of a cyclist completing $7$ rounds in a minute along a circular track of radius $5 \,m$ with a constant speed, is ……… $m / s ^2$

medium

A tachometer is a device to measure

easy

Motion in two dimensions, in a plane can be studied by expressing position, velocity and acceleration as vectors in cartesian co-ordinates $A=A_{x} \hat{i}+A_{y} \hat{j},$ where $\hat{i}$ and $\hat{\jmath}$ are unit vector along $x$ and $y$ – directions, respectively and $A_{x}$ and $A_{y}$ are corresponding components of $A$. Motion can also be studied by expressing vectors in circular polar co-ordinates as $\overrightarrow A \, = \,{A_r}\widehat r\,\, + \,{A_\theta }\hat \theta $ where $\hat{r}=\frac{r}{r}=\cos \theta \hat{i}+\sin \theta \hat{\jmath}$ and $\hat{\theta}=-\sin \theta \hat{i}+\cos \theta \hat{j}$ are unit vectors along direction in which $\hat{r}$ and $\hat{\theta}$ are increasing.
$(a)$ Express ${\widehat {i\,}}$ and ${\widehat {j\,}}$ in terms of ${\widehat {r\,}}$ and ${\widehat {\theta }}$ .
$(b)$ Show that both $\widehat r$ and $\widehat \theta $ are unit vectors and are perpendicular to each other.
$(c)$ Show that $\frac{d}{{dr}}(\widehat r)\, = \,\omega \hat \theta \,$, where $\omega \, = \,\frac{{d\theta }}{{dt}}$ and $\frac{d}{{dt}}(\widehat \theta )\, = \, – \theta \widehat r\,$.
$(d)$ For a particle moving along a spiral given by $\overrightarrow r \, = \,a\theta \widehat r$, where $a = 1$ (unit), find dimensions of $a$.
$(e)$ Find velocity and acceleration in polar vector representation for particle moving along spiral described in $(d)$ above.

hard

A stone tied to $180 cm$ long string at its end is making 28 revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is $\frac{1936}{ x }\,ms ^{-2}$. The value of $x.........\left(\text { Take } \pi=\frac{22}{7}\right)$

Solution

Similar Questions

A stone ties to the end of a string $1\,m$ long is whirled in a horizontal circle with a constant speed. If the stone makes $22$ revolution in $44$ seconds, what is the magnitude and direction of acceleration of the stone

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