Motion of the Centre of Mass

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Other Competitive Exams

NDA

MATHS

Courses

Class Room Courses
Online Live Courses
Online Recorded Courses

ONLINE COURSES

Q 1 :

In a system, two particles of masses $m_{1} = 3$ kg and $m_{2} = 2$ kg are placed at a certain distance from each other. The particle of mass $m_{1}$ is moved towards the center of mass of the system through a distance of 2 cm. In order to keep the center of mass of the system at the original position, the particle of mass $m_{2}$ should move towards the center of mass by the distance ___ cm. [2024]

(3)

$Δ X_{C.O.M} = \frac{m_{1} Δ x_{1} + m_{2} Δ x_{2}}{m_{1} + m_{2}}$

$0 = \frac{3 \times 2 + 2 (- x)}{3 + 2} \Rightarrow x = 3 cm$

Q 2 :

Two identical bodies A and B of equal masses have initial velocities ${\vec{v}}_{1} = 4 \hat{i} m / s$ and ${\vec{v}}_{2} = 4 \hat{j} m / s$ respectively. The body A has acceleration ${\vec{a}}_{1} = 6 \hat{i} + 6 \hat{j} m / s^{2}$ while the acceleration of the other body B is zero. The centre of mass of the two bodies moves in ______ path. [2026]

circular
parabolic
straight line
elliptical

(3)

${\vec{v}}_{cm} = \frac{m_{1} {\vec{v}}_{1} + m_{2} {\vec{v}}_{2}}{m_{1} + m_{2}} = \frac{m (4 \hat{i}) + m (4 \hat{j})}{2 m} = (2 \hat{i} + 2 \hat{j}) m / s$

${\vec{a}}_{cm} = \frac{m_{1} {\vec{a}}_{1} + m_{2} {\vec{a}}_{2}}{m_{1} + m_{2}} = \frac{m (6 \hat{i} + 6 \hat{j}) + m (0)}{2 m} = 3 \hat{i} + 3 \hat{j}$

${\vec{v}}_{cm} and {\vec{a}}_{cm} are along same line so path is a straight line.$

Topic Question Set

Want Us to Email you About Special Offers & Updates?

Topic Question Set

Q 2 : Two identical bodies A and B of equal masses have initial velocities v→1=4i^ m/s and v→2=4j^ m/s respectively. The body A has acceleration a→1=6i^+6j^ m/s2 while the acceleration of the other body B is zero. The centre of mass of the two bodies moves in ______ path. [2026]

Want Us to Email you About Special Offers & Updates?