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

Question

There are four particles A,B,C and D with masses mA=m,mB=2 m,mC=3 m and mD=4 m are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the center of mass of the particles is: <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-sydrekcjm5p2p16m.jpg" /> (A) (a/5)(. hati- hatj.) (B) (a/5)(. hati+ hatj.) (C) a(. hati+ hatj.) (D) Zero

Tardigrade Admin · Accepted Answer

∴ overset arrow acm=(m1 overset arrow a1 + m2 overset arrow a2 + ldots /m1 + m2 + ldots ) =(m × (. - a hati .) + 2 m (. a hatj .) + 3 m (. a hati .) + 4 m (. - a hatj .)/m + 2 m + 3 m + 4 m)=((2 hati - 2 hatj/10))a=(a/5)(. hati- hatj.)

Q. There are 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 center of mass of the particles is:

$\frac{a}{5} (\hat{i} - \hat{j})$

$\frac{a}{5} (\hat{i} + \hat{j})$

$a (\hat{i} + \hat{j})$

Zero

$∴ a \to_{c m} = \frac{m _{1} a \to _{1} + m _{2} a \to _{2} + \dots}{m _{1} + m _{2} + \dots}$
$= \frac{m \times ( - a i ^ ) + 2 m ( a j ^ ) + 3 m ( a i ^ ) + 4 m ( - a j ^ )}{m + 2 m + 3 m + 4 m} = (\frac{2 i ^ - 2 j ^}{10}) a = \frac{a}{5} (\hat{i} - \hat{j})$

Q. There are 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 center of mass of the particles is:

5a​(i^−j^​)

5a​(i^+j^​)

a(i^+j^​)