You visited us 1 times! Enjoying our articles? Unlock Full Access!

Com of Solid Bodies

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 is

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

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

\frac{a}{5} (^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!

a (^i +^j)

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

Open in App

Solution

The correct option is A $\frac{a}{5} (^i -^j)$

${\to a}_{A} = - a^i$
${\to a}_{B} = a^j$
${\to a}_{C} = a^i$
${\to a}_{D} = - a^j$
${\to a}_{c m} = \frac{m_{a} {\to a}_{a} + m_{b} {\to a}_{b} + m_{c} {\to a}_{c} + m_{d} {\to a}_{d}}{m_{a} + m_{b} + m_{c} + m_{d}}$
${\to a}_{c m} = \frac{- m a^i + 2 m a \to j + 3 m a^i - 4 m a^j}{10 m}$
$= \frac{2 m a^i - 2 m a^j}{10 m}$
$= \frac{a}{5}^i - \frac{a}{5}^j$
$= \frac{a}{5} (^i -^j)$ .

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. The acceleration of the centre of mass of the particles 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 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}

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

Q. Four particles of masses

m, 2 m, 3 m

, and

4 m

respectively are placed at the corners of a square of side a, as shown in the figure. 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 is

The correct option is A a5(^i−^j) →aA=−a^i →aB=a^j →aC=a^i →aD=−a^j →acm=ma→aa+mb→ab+mc→ac+md→adma+mb+mc+md →acm=−ma^i+2ma→j+3ma^i−4ma^j10m =2ma^i−2ma^j10m =a5^i−a5^j =a5(^i−^j).

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