What are the co-ordinates of the centre of mass of the three-particle system shown in fig.?

Question

What are the co-ordinates of the centre of mass of the three-particle system shown in fig.? <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/ea116db6bf61367d71c09715381c6f5f-.png" /> (A) x=1.1 m , y=1.3 m (B) x=0.7 m , y=0.8 m (C) x=0.5 m , y=0.6 m (D) x=0 m , y=3 m

Tardigrade Admin · Accepted Answer

x cm =((3 kg )(0 m )+(8 kg )(1 m )+(4 kg )(2 m )/(3 kg +8 kg +4 kg )) =(16 kg m /15 kg ) ≈ 1.1 m y cm =((3 kg )(0 m )+(8 kg )(2 m )+(4 kg )(1 m )/(3 kg +8 kg +4 kg )) =(20 kg m /15 kg ) ≈ 1.3 m

Q. What are the co-ordinates of the centre of mass of the three-particle system shown in fig.?

$x = 1.1 m, y = 1.3 m$

$x = 0.7 m, y = 0.8 m$

$x = 0.5 m, y = 0.6 m$

$x = 0 m, y = 3 m$

$x_{c m} = \frac{( 3 k g ) ( 0 m ) + ( 8 k g ) ( 1 m ) + ( 4 k g ) ( 2 m )}{( 3 k g + 8 k g + 4 k g )}$
$= \frac{16 k g m}{15 k g} \approx 1.1 m$
$y_{c m} = \frac{( 3 k g ) ( 0 m ) + ( 8 k g ) ( 2 m ) + ( 4 k g ) ( 1 m )}{( 3 k g + 8 k g + 4 k g )}$
$= \frac{20 k g m}{15 k g} \approx 1.3 m$

Q. What are the co-ordinates of the centre of mass of the three-particle system shown in fig.?

x=1.1m,y=1.3m

x=0.7m,y=0.8m

x=0.5m,y=0.6m

x=0m,y=3m

xcm​=(3kg+8kg+4kg)(3kg)(0m)+(8kg)(1m)+(4kg)(2m)​ =15kg16kgm​≈1.1m ycm​=(3kg+8kg+4kg)(3kg)(0m)+(8kg)(2m)+(4kg)(1m)​ =15kg20kgm​≈1.3m

$x = 1.1 m, y = 1.3 m$

$x = 0.7 m, y = 0.8 m$

$x = 0.5 m, y = 0.6 m$

$x = 0 m, y = 3 m$

$x_{c m} = \frac{( 3 k g ) ( 0 m ) + ( 8 k g ) ( 1 m ) + ( 4 k g ) ( 2 m )}{( 3 k g + 8 k g + 4 k g )}$
$= \frac{16 k g m}{15 k g} \approx 1.1 m$
$y_{c m} = \frac{( 3 k g ) ( 0 m ) + ( 8 k g ) ( 2 m ) + ( 4 k g ) ( 1 m )}{( 3 k g + 8 k g + 4 k g )}$
$= \frac{20 k g m}{15 k g} \approx 1.3 m$