Two particles of equal mass have velocities 2 | vedclass

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

Question

(D) Given,masses $m_1 = m_2 = m$.Initial velocities are $\vec{v}_1 = 2\hat{i}\,ms^{-1}$ and $\vec{v}_2 = 2\hat{j}\,ms^{-1}$.Accelerations are $\vec{a}

Vedclass · Accepted Answer

straight line

Vedclass · Answer

(D) Given,masses $m_1 = m_2 = m$.Initial velocities are $\vec{v}_1 = 2\hat{i}\,ms^{-1}$ and $\vec{v}_2 = 2\hat{j}\,ms^{-1}$.Accelerations are $\vec{a}_1 = (3\hat{i} + 3\hat{j})\,ms^{-2}$ and $\vec{a}_2 = 0$.The velocity of the centre of mass is $\vec{v}_{CM} = \frac{m_1\vec{v}_1 + m_2\vec{v}_2}{m_1 + m_2} = \frac{m(2\hat{i} + 2\hat{j})}{2m} = (\hat{i} + \hat{j})\,ms^{-1}$.The acceleration of the centre of mass is $\vec{a}_{CM} = \frac{m_1\vec{a}_1 + m_2\vec{a}_2}{m_1 + m_2} = \frac{m(3\hat{i} + 3\hat{j} + 0)}{2m} = \frac{3}{2}(\hat{i} + \hat{j})\,ms^{-2}$.Since the initial velocity vector $\vec{v}_{CM} = (\hat{i} + \hat{j})$ and the acceleration vector $\vec{a}_{CM} = \frac{3}{2}(\hat{i} + \hat{j})$ are parallel (i.e.,$\vec{a}_{CM} = k\vec{v}_{CM}$ where $k = 1.5$),the centre of mass moves in a straight line.

Two particles of equal mass have velocities $2\,\hat{i}\,ms^{-1}$ and $2\,\hat{j}\,ms^{-1}$. The first particle has an acceleration $(3\,\hat{i} + 3\,\hat{j})\,ms^{-2}$ while the acceleration of the second particle is zero. The centre of mass of the two particles moves in

Similar Questions

Two particles of mass $m_1$ and $m_2$ are separated by a distance $d$. If the first particle is moved towards the centre of mass by a distance $x$,then the distance by which the second particle must be moved towards the centre of mass to keep the centre of mass at the same position is:

The figure shows a man of mass $m$ standing at the end $A$ of a trolley of mass $M$ placed at rest on a smooth horizontal surface. The man starts moving towards the end $B$ with a velocity $u_{rel}$ with respect to the trolley. The length of the trolley is $L$. Choose the correct statement.

Two particles $A$ and $B$,initially at rest,move towards each other under a mutual force of attraction. At the instant when the speed of $A$ is $v$ and the speed of $B$ is $2v$,the speed of the center of mass of the system is:

Two masses $m_1$ and $m_2$ $(m_1 > m_2)$ are connected by a massless,flexible,and inextensible string passed over a massless and frictionless pulley. The acceleration of the center of mass of the system is

The centre of mass of two masses $m$ and $m'$ moves by a distance $\frac{x}{5}$ when mass $m$ is moved by a distance $x$ and $m'$ is kept fixed. The ratio $\frac{m'}{m}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module