(A) Given: $m_1 = 2 \ kg$,$m_2 = 1 \ kg$,$u_1 = 2 \ m/s$,$u_2 = 5 \ m/s$. Case $1$: Both particles move in the same direction. The velocity of the cen

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

(A) Given: $m_1 = 2 \ kg$,$m_2 = 1 \ kg$,$u_1 = 2 \ m/s$,$u_2 = 5 \ m/s$. Case $1$: Both particles move in the same direction. The velocity of the centre of mass is $v_{cm} = \frac{m_1 u_1 + m_2 u_2}{m_1 + m_2} = \frac{2(2) + 1(5)}{2 + 1} = \frac{4 + 5}{3} = 3 \ m/s$. So,$v_1 = 3 \ m/s$. Case $2$: Both particles move in opposite directions. Let $u_1 = 2 \ m/s$ and $u_2 = -5 \ m/s$. The velocity of the centre of mass is $v_{cm} = \frac{m_1 u_1 + m_2 u_2}{m_1 + m_2} = \frac{2(2) + 1(-5)}{2 + 1} = \frac{4 - 5}{3} = -1/3 \ m/s$. The speed is the magnitude of velocity,so $v_2 = |-1/3| = 1/3 \ m/s$.

Class 11 Physics System of Particles and Rotational Motion Motion of Centre of Mass

Medium

Two particles of masses $2 \ kg$ and $1 \ kg$ are moving along the same line with speeds of $2 \ m/s$ and $5 \ m/s$ respectively. If both particles are moving in the same direction,the speed of the centre of mass is $v_1$. If both particles are moving in opposite directions,the speed of the centre of mass is $v_2$. Find $v_1$ and $v_2$.

A
$3 \ m/s, \ 1/3 \ m/s$
B
$1/3 \ m/s, \ 3 \ m/s$
C
$2 \ m/s, \ 1/2 \ m/s$
D
$1/2 \ m/s, \ 2 \ m/s$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

System of Particles and Rotational Motion

Subtopic

Motion of Centre of Mass

Two particles of masses $2 \ kg$ and $3 \ kg$ are moving along the $X$-axis with velocities $3 \ m/s$ and $2 \ m/s$ respectively. The velocity of the center of mass of this system is ........ $m/s$.

Medium

View Solution

If a gas is filled in a stationary sphere,its molecules are in random motion due to thermal energy. Will the center of mass of these molecules be in motion?

Easy

View Solution

$A$ boy of mass $20\, kg$ is standing on an $80\, kg$ cart that is free to move. There is negligible friction between the cart and the ground. Initially,the boy is standing $25\, m$ from a wall. If he walks $10\, m$ on the cart towards the wall,then the final distance of the boy from the wall will be ........ $m$

DifficultJEE MAIN 2013

View Solution

Two blocks of masses $5 \,kg$ and $2 \,kg$ are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of $7 \,m/s$ to the heavier block in the direction of the lighter block. The velocity of the centre of mass is ....... $m/s$.

Easy

View Solution

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 $L$. The distance moved by the man with respect to ground is

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

Similar Questions

Two particles of masses $2 \ kg$ and $3 \ kg$ are moving along the $X$-axis with velocities $3 \ m/s$ and $2 \ m/s$ respectively. The velocity of the center of mass of this system is ........ $m/s$.

If a gas is filled in a stationary sphere,its molecules are in random motion due to thermal energy. Will the center of mass of these molecules be in motion?

Two blocks of masses $5 \,kg$ and $2 \,kg$ are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of $7 \,m/s$ to the heavier block in the direction of the lighter block. The velocity of the centre of mass is ....... $m/s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module