Question:
An insect trapped in a circular groove of radius $12\,cm$ moves along the groove steadily and completes $7$ revolutions in $100\,s$. The linear speed of the insect is
An insect trapped in a circular groove of radius $12\,cm$ moves along the groove steadily and completes $7$ revolutions in $100\,s$. The linear speed of the insect is
Updated On: Jul 6, 2022
- $4.3\,cms^{-1}$
- $5.3\,cms^{-1}$
- $6.3\,cms^{-1}$
- $7.3\,cms^{-1}$
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The Correct Option is B
Solution and Explanation
Here, $r = 12\, cm$, frequency, $\upsilon=\frac{7}{100}rps$
The angular speed of the insect is
$\omega=2\pi\upsilon=2\pi\times\frac{7}{100}=0.44\,rad\,s^{-1}$
The linear speed of the insect is $v= \omega r=0.44 \times 12$
$ = 5.3\, cm s^{-1}$
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Notes on Motion in a plane
Concepts Used:
Motion in a Plane
It is a vector quantity. A vector quantity is a quantity having both magnitude and direction. Speed is a scalar quantity and it is a quantity having a magnitude only. Motion in a plane is also known as motion in two dimensions.
Equations of Plane Motion
The equations of motion in a straight line are:
v=u+at
s=ut+½ at2
v2-u2=2as
Where,
- v = final velocity of the particle
- u = initial velocity of the particle
- s = displacement of the particle
- a = acceleration of the particle
- t = the time interval in which the particle is in consideration