Three masses 2 kg, 3 kg and 4 kg are lying at the corners of an equilateral triangle of side l . The X coordinate of center of mass is

Question

Three masses 2 kg, 3 kg and 4 kg are lying at the corners of an equilateral triangle of side l . The X coordinate of center of mass is <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-pp5dbmsd8rmz.png" /> (A) (7/12)l (B) (5/9)l (C) (7 √2/9)l (D) (√5/9)l

Tardigrade Admin · Accepted Answer

The (X) coordinate of center of mass is, Xc m=(m1 x1 + m2 x2 + m3 x3/m1 + m2 + m3) Xc m=(2 (0) + 3 l + 4 ((l/2))/2 + 3 + 4) Xc m=(5/9)l

Q. Three masses $2 k g, 3 k g$ and $4 k g$ are lying at the corners of an equilateral triangle of side $l$ . The $X$ coordinate of center of mass is

$\frac{7}{12} l$

$\frac{5}{9} l$

$\frac{7 2}{9} l$

$\frac{5}{9} l$

The $(X)$ coordinate of center of mass is,
$X_{c m} = \frac{m _{1} x _{1} + m _{2} x _{2} + m _{3} x _{3}}{m _{1} + m _{2} + m _{3}}$
$X_{c m} = \frac{2 ( 0 ) + 3 l + 4 ( \frac{l}{2} )}{2 + 3 + 4}$
$X_{c m} = \frac{5}{9} l$

Q. Three masses 2kg,3kg and 4kg are lying at the corners of an equilateral triangle of side l . The X coordinate of center of mass is

127​l

95​l

972​​l

95​​l

The (X) coordinate of center of mass is, Xcm​=m1​+m2​+m3​m1​x1​+m2​x2​+m3​x3​​ Xcm​=2+3+42(0)+3l+4(2l​)​ Xcm​=95​l

Q. Three masses $2 k g, 3 k g$ and $4 k g$ are lying at the corners of an equilateral triangle of side $l$ . The $X$ coordinate of center of mass is

$\frac{7}{12} l$

$\frac{5}{9} l$

$\frac{7 2}{9} l$

$\frac{5}{9} l$

The $(X)$ coordinate of center of mass is,
$X_{c m} = \frac{m _{1} x _{1} + m _{2} x _{2} + m _{3} x _{3}}{m _{1} + m _{2} + m _{3}}$
$X_{c m} = \frac{2 ( 0 ) + 3 l + 4 ( \frac{l}{2} )}{2 + 3 + 4}$
$X_{c m} = \frac{5}{9} l$