Question:
A particle moves in a circle of radius $5 \,cm$ with constant speed and time period $0.2 \,\pi\, s$. The acceleration of the particle is
A particle moves in a circle of radius $5 \,cm$ with constant speed and time period $0.2 \,\pi\, s$. The acceleration of the particle is
Updated On: May 4, 2024
- $15 \,m/s^2 $
- $25 \,m/s^2 $
- $36 \,m/s^2 $
- $5 \, m/s^2 $
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The Correct Option is D
Solution and Explanation
If particle move in a circular path with constant speed, the acceleration of the particle is centripetal acceleration
$a _{ c }=\omega^{2} R =\left(\frac{2 \pi}{ T }\right)^{2}\, R$
$a _{ c }=\frac{4 \pi^{2} R }{ T ^{2}}=\frac{4 \pi^{2}}{(0.2 \pi)^{2}} \times 5 \times 10^{-2}$
$a _{ c }=5 \,m / \,sec ^{2}$
$a _{ c }=\omega^{2} R =\left(\frac{2 \pi}{ T }\right)^{2}\, R$
$a _{ c }=\frac{4 \pi^{2} R }{ T ^{2}}=\frac{4 \pi^{2}}{(0.2 \pi)^{2}} \times 5 \times 10^{-2}$
$a _{ c }=5 \,m / \,sec ^{2}$
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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