The figure below shows a body of mass M movin | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) In uniform circular motion,the magnitude of centripetal acceleration is $a = \frac{v^2}{R}$.At point $P_1$,the acceleration vector $\vec{a}_1$ is

Vedclass · Accepted Answer

$\frac{{{v^2}}}{R} \sqrt 2 $

Vedclass · Answer

(D) In uniform circular motion,the magnitude of centripetal acceleration is $a = \frac{v^2}{R}$.At point $P_1$,the acceleration vector $\vec{a}_1$ is directed towards the center,i.e.,$\vec{a}_1 = \frac{v^2}{R} \hat{i}$.At point $P_2$,the acceleration vector $\vec{a}_2$ is directed towards the center,i.e.,$\vec{a}_2 = \frac{v^2}{R} \hat{j}$.The change in acceleration is $\Delta \vec{a} = \vec{a}_2 - \vec{a}_1 = \frac{v^2}{R} \hat{j} - \frac{v^2}{R} \hat{i}$.The magnitude of the change in acceleration is $|\Delta \vec{a}| = \sqrt{(\frac{v^2}{R})^2 + (-\frac{v^2}{R})^2} = \sqrt{2(\frac{v^2}{R})^2} = \frac{v^2}{R} \sqrt{2}$.

The figure below shows a body of mass $M$ moving with a uniform speed $v$ on a circular path of radius $R$. What is the change in acceleration when moving from point $P_1$ to $P_2$?

Similar Questions

An object moves at a constant speed along a circular path in the horizontal $XY$ plane with the center at the origin. When the object is at $x = -2 \, m$,its velocity is $-(4 \, m/s) \hat{j}$. What is the object's acceleration when it is at $y = 2 \, m$?

Write the equation for centripetal acceleration in uniform circular motion. Obtain these equations in terms of angular velocity $(\omega)$ and frequency $(\nu)$.

$A$ merry-go-round rotating at a constant angular speed completes $9$ rotations in $18$ seconds. What is its angular speed?

$A$ particle executing uniform circular motion has:

What is uniform circular motion? By using a proper figure,derive the equation for centripetal acceleration $a_c = \frac{v^2}{r}$ for uniform circular motion. Show that its direction is towards the center.

Vedclass Test Series

Exam Paper Generator

Online Exam Module