Three particles A, B and C of masses m, 2m an | vedclass

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

Question

(B) Given masses are $m_1 = m$, $m_2 = 2m$, and $m_3 = 3m$.The velocities are directed as follows:Particle $A$ moves north: $\vec{v}_1 = 6 \hat{j} \,m

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(B) Given masses are $m_1 = m$, $m_2 = 2m$, and $m_3 = 3m$.The velocities are directed as follows:Particle $A$ moves north: $\vec{v}_1 = 6 \hat{j} \,ms^{-1}$Particle $B$ moves south: $\vec{v}_2 = -12 \hat{j} \,ms^{-1}$Particle $C$ moves east: $\vec{v}_3 = 8 \hat{i} \,ms^{-1}$The velocity of the centre of mass $\vec{v}_{cm}$ is given by:$\vec{v}_{cm} = \frac{m_1 \vec{v}_1 + m_2 \vec{v}_2 + m_3 \vec{v}_3}{m_1 + m_2 + m_3}$Substituting the values:$\vec{v}_{cm} = \frac{m(6 \hat{j}) + 2m(-12 \hat{j}) + 3m(8 \hat{i})}{m + 2m + 3m}$$\vec{v}_{cm} = \frac{6m \hat{j} - 24m \hat{j} + 24m \hat{i}}{6m}$$\vec{v}_{cm} = \frac{24m \hat{i} - 18m \hat{j}}{6m} = 4 \hat{i} - 3 \hat{j} \,ms^{-1}$The magnitude of the velocity of the centre of mass is:$v_{cm} = \sqrt{(4)^2 + (-3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \,ms^{-1}$

Similar Questions

Two particles have masses $m_1$ and $m_2$. If the first particle $(m_1)$ is moved by a distance $d$ towards the center of mass,by what distance should the second particle $(m_2)$ be moved so that the center of mass of the system remains at the same position?

$30 \,kg$ boy stands at the far edge of a floating plank, whose near edge is against the shore of a river. The plank is $10 \,m$ long and weighs $10 \,kg$. If the boy walks to the near edge of the plank, how far from the shore does the plank move (in $\,m$)?

$A$ man of mass $m$ is suspended in air by holding the rope of a balloon of mass $M$. As the man climbs up the rope,the balloon

$A$ ball of mass $1\, kg$ is thrown up with an initial speed of $4\, m/s$. $A$ second ball of mass $2\, kg$ is released from rest from some height as shown in the figure. Select the correct alternative.

Vedclass Test Series

Exam Paper Generator

Online Exam Module