Consider a two-particle system with particles | vedclass

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

Question

(D) The position of the centre of mass $R_{cm}$ is given by $R_{cm} = \frac{m_1 r_1 + m_2 r_2}{m_1 + m_2}$.For the centre of mass to remain at the sam

Vedclass · Accepted Answer

$\left( \frac{m_1}{m_2} \right) d$

Vedclass · Answer

(D) The position of the centre of mass $R_{cm}$ is given by $R_{cm} = \frac{m_1 r_1 + m_2 r_2}{m_1 + m_2}$.For the centre of mass to remain at the same position,the change in the position of the centre of mass must be zero,i.e.,$\Delta R_{cm} = 0$.Therefore,$m_1 \Delta r_1 + m_2 \Delta r_2 = 0$.Given that the first particle is moved by a distance $d$ towards the centre of mass,let $\Delta r_1 = d$.Substituting this into the equation: $m_1 d + m_2 \Delta r_2 = 0$.Solving for $\Delta r_2$: $\Delta r_2 = -\left( \frac{m_1}{m_2} \right) d$.The negative sign indicates that the second particle must be moved in the opposite direction to the first particle,also towards the centre of mass,by a distance of $\left( \frac{m_1}{m_2} \right) d$.

Consider a two-particle system with particles having masses $m_1$ and $m_2$. If the first particle is pushed towards the centre of mass through a distance $d$,by what distance should the second particle be moved,so as to keep the centre of mass at the same position?

Similar Questions

Two blocks of mass $m$ each,connected to each other by a massless string,are placed on two inclined planes as shown in the figure. After releasing from rest,find the magnitude of the acceleration of the centre of mass of both the blocks. (Given $g = 10 \, m/s^2$)

$A$ $500\,kg$ boat is $9\,m$ long and is floating without motion on still water. $A$ man of mass $100\,kg$ is at one end and if he runs to the other end of the boat and stops,the displacement of the boat is

Obtain Newton's second law for a system of particles and write its statement.

Two particles $A$ and $B$,initially at rest,move towards each other under a mutual force of attraction. At an instance when the speed of $A$ is $v$ and the speed of $B$ is $2v$,the speed of the centre of mass $(CM)$ is:

$A$ ball of mass $m$ is thrown upward and another ball of same mass is thrown downward so as to move freely under gravity. The acceleration of the centre of mass is .........

Vedclass Test Series

Exam Paper Generator

Online Exam Module