You visited us 3 times! Enjoying our articles? Unlock Full Access!

Displacement of COM:Application

Four particle...

Question

Four particles A,B,C and D with masses $m_{A} = m, m_{B} = 2 m, m_{C} = 3 m$ and $m_{D} = 4 m$ are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles in ${ms}^{- 2}$ is

\frac{a}{5} (^i -^j)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

a (^i +^j)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Zero

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{a}{5} (^i +^j)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{a}{5} (^i -^j)$
For a system of discrete masses, acceleration of centre of mass (CM) is given by
$a_{C M} = \frac{m_{A} a_{A} + m_{B} a_{B} + m_{C} a_{C} + m_{D} a_{D}}{m_{A} + m_{B} + m_{C} + m_{D}}$

where, $m_{A} = m, m_{B} = 2 m, m_{C} = 3 m$ and $m_{D} = 4 m$ ,
$| a_{A} | = | a_{B} | = | a_{C} | = | a_{D} | = a$ (according to the question)
$_{C M} = \frac{- m a^i + 2 m a^j + 3 m a^i - 4 m a^j}{m + 2 m + 3 m + 4 m}$
$= \frac{2 a^i - 2 a^j}{10} = \frac{a}{5} . (^i -^j) {ms}^{- 2}$

Suggest Corrections

Similar questions

Q. Four particles

A

B

C

and

D

with masses

m_{a} = m, m_{B} = 2 m, m_{C} = 3 m

and

m_{D} = 4 m

are at the corners of a square. They have accelerations of equal magnitude with directions as shown in the figure. The acceleration of centre of mass of the particles (in

{ms}^{- 2}

) is :

Q. Four particles

A

B

C

and

D

with masses

m_{a} = m, m_{B} = 2 m, m_{C} = 3 m

and

m_{D} = 4 m

are at the corners of a square. They have accelerations of equal magnitude with directions as shown in the figure. The acceleration of centre of mass of the particles (in

{ms}^{- 2}

) is :

Q. Four particles are placed at the corners of a square as shown in figure. Acceleration of the centre of mass of the particle (in

{m/s}^{2}

) is

Q. Four particles

A, B, C

and

D

with masses

m_{A} = m, m_{B} = 2 m, m_{C} = 3 m

and

m_{D} = 4 m

are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is

Four particles $A$ , $B$ , $C$ and $D$ having masses $m$ , $2 m$ , $3 m$ and $4 m$ respectively are placed in order at the corners of a square of side $a$ . Locate the centre of mass

Join BYJU'S Learning Program

Four particles A,B,C and D with masses mA=m,mB=2m,mC=3m and mD=4m are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles in ms−2 is

Four particles A,B,C and D with masses $m_{A} = m, m_{B} = 2 m, m_{C} = 3 m$ and $m_{D} = 4 m$ are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles in ${ms}^{- 2}$ is