Question:
Figure shows a body of mass m moving with a uniform speed $v$ along a circle of radius $r$. The change in velocity in going from $A$ to $B$ is:
Figure shows a body of mass m moving with a uniform speed $v$ along a circle of radius $r$. The change in velocity in going from $A$ to $B$ is:
Updated On: Jun 18, 2022
- $ v\sqrt{2} $
- $ v/\sqrt{2} $
- $ v $
- zero
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
When a body rotates uniformly, then the direction of velocity changes continuously but its magnitude remains constant.
Also, direction of velocity is perpendicular to direction of motion.
$\therefore \vec{v}_{A}=\hat{j} \vec{v}$
$\vec{v}_{B}=-\hat{i} \vec{v}$
Change in velocity
$\Delta \vec{v}=\vec{v}_{B}-\vec{v}_{A}$
$=-\hat{i} \vec{v}-\hat{j} \vec{v}$
Magnitude of change in velocity is
$=|-\hat{i} \vec{v}-\hat{j} \vec{v}|$
$=\sqrt{v^{2}+v^{2}}=v \sqrt{2}$
Also, direction of velocity is perpendicular to direction of motion.
$\therefore \vec{v}_{A}=\hat{j} \vec{v}$
$\vec{v}_{B}=-\hat{i} \vec{v}$
Change in velocity
$\Delta \vec{v}=\vec{v}_{B}-\vec{v}_{A}$
$=-\hat{i} \vec{v}-\hat{j} \vec{v}$
Magnitude of change in velocity is
$=|-\hat{i} \vec{v}-\hat{j} \vec{v}|$
$=\sqrt{v^{2}+v^{2}}=v \sqrt{2}$
Was this answer helpful?
0
0
Top Questions on Motion in a plane
- The resultant of two vectors \( \vec{A} \) and \( \vec{B} \) is perpendicular to \( \vec{A} \) and its magnitude is half that of \( \vec{B} \). The angle between vectors \( \vec{A} \) and \( \vec{B} \) is ________ .
- JEE Main - 2024
- Physics
- Motion in a plane
- If two vectors \(\vec{A}\) and \(\vec{B}\) having equal magnitude \(R\) are inclined at an angle \(\theta\), then
- JEE Main - 2024
- Physics
- Motion in a plane
- A ball dropped from a bridge hits the surface of the water in 3 𝑠. The height of the bridge, ignoring air resistance, is ___ 𝑚 (rounded off to one decimal place). (Use $𝑔 = 9.8 𝑚𝑠^{−2}$)
- IIT JAM BT - 2024
- Physics
- Motion in a plane
- A bullet is fired from a gun at the speed of 280 ms-1 in the direction 30° above the horizontal. The maximum height attained by the bullet is
(g = 9.8 ms-2, sin 30° = 0.5)- NEET (UG) - 2023
- Physics
- Motion in a plane
Car P is heading east with a speed V and car Q is heading north with a speed \(\sqrt{3}\). What is the velocity of car Q with respect to car P?
- KEAM - 2023
- Physics
- Motion in a plane
View More Questions
Questions Asked in DUET exam
- A hammer of mass $200\, kg$ strikes a steel block of mass $200\, g$ with a velocity $8\, ms^{-1}$. If $23\%$ of the energy is utilized to heat the steel block, the rise in temperature of the block is (specific heat capacity of steel = $460 \; J \; kg^{-1} \; K^{-1}$)
- DUET - 2019
- specific heat capacity
- What is the shape and magnetic nature of permanganate ion ?
- DUET - 2019
- d -and f -Block Elements
- The mobility of charge carriers increases with
- DUET - 2011
- Electric Current
- Phagocytosis and pinocytosis are collectively termed as
- DUET - 2011
- Cell: the unit of life
- How many $ 1\,\mu F $ capacitors must be connected in parallel to store a charge of $1\, C$ with a potential of $110\, V$ across the capacitors?
- DUET - 2011
- electrostatic potential and capacitance
View More Questions
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