Question:
A body moving along a circular path of radius $R$ with velocity $v$, has centripetal acceleration a. If its velocity is made equal to $2v$, then its centripetal acceleration is
A body moving along a circular path of radius $R$ with velocity $v$, has centripetal acceleration a. If its velocity is made equal to $2v$, then its centripetal acceleration is
Updated On: Jun 3, 2024
- $ 4\,a $
- $ 2\,a $
- $ \frac{a}{4} $
- $ \frac{a}{2} $
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The Correct Option is A
Solution and Explanation
The centripetal acceleration $a=\frac{v^{2}}{R}$
or $a \propto v^{2}$
or $\frac{a_{1}}{a_{2}}=\frac{v_{1}^{2}}{v_{2}^{2}}$
$=\frac{a}{a_{2}}=\frac{v^{2}}{(2 v)^{2}}=\frac{1}{4}$
or $a_{2}=4\, a$
or $a \propto v^{2}$
or $\frac{a_{1}}{a_{2}}=\frac{v_{1}^{2}}{v_{2}^{2}}$
$=\frac{a}{a_{2}}=\frac{v^{2}}{(2 v)^{2}}=\frac{1}{4}$
or $a_{2}=4\, a$
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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