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3-2.Motion in Plane
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कोई कीड़ा एक वृत्तीय खाँचे में जिसकी त्रिज्या $12\, cm$ है, फँँस गया है । वह खाँचे के अनुदिश स्थिर चाल से चलता है और $100$ सेकंड में $7$ चक्कर लगा लेता है।
$(a)$ कीड़े की कोणीय चाल व रैखिक चाल कितनी होगी ?
$(b)$ क्या त्वरण सदिश एक अचर सदिश है। इसका परिणाम कितना होगा ?
Option A
Option B
Option C
Option D
Solution
Answer This is an example of uniform circular motion. Here $R=12 cm .$ The angular speed $\omega$ is given by
$\omega=2 \pi / T=2 \pi \times 7 / 100=0.44 rad / s$
The linear speed $v$ is :
$v=\omega R=0.44 s ^{-1} \times 12 cm =5.3 cm s ^{-1}$
The direction of velocity $v$ is along the tangent to the circle at every point. The acceleration is directed towards the centre of the circle. since this direction changes continuously. acceleration here is not a constant vector. However, the magnitude of acceleration is constant:
$a=\omega^{2} R=\left(0.44 s ^{-1}\right)^{2}(12 cm )$
$=2.3 cm s ^{-2}$
$\omega=2 \pi / T=2 \pi \times 7 / 100=0.44 rad / s$
The linear speed $v$ is :
$v=\omega R=0.44 s ^{-1} \times 12 cm =5.3 cm s ^{-1}$
The direction of velocity $v$ is along the tangent to the circle at every point. The acceleration is directed towards the centre of the circle. since this direction changes continuously. acceleration here is not a constant vector. However, the magnitude of acceleration is constant:
$a=\omega^{2} R=\left(0.44 s ^{-1}\right)^{2}(12 cm )$
$=2.3 cm s ^{-2}$
Standard 11
Physics
