If three particles of masses 2kg, 1kg and 3 kg are placed at comers of an equilateral triangle of perimeter 6m then the distance of center of mass which is at origin of particles from 1kg mass is (approximately) (Assume 2kg on x-axis )

Question

If three particles of masses 2kg, 1kg and 3 kg are placed at comers of an equilateral triangle of perimeter 6m then the distance of center of mass which is at origin of particles from 1kg mass is (approximately) (Assume 2kg on x-axis ) (A) √6m (B) √2m (C) (1/√2)m (D) 2m

Tardigrade Admin · Accepted Answer

Co-ordinates o f 1 kg, 2 kg, 3 kg are (0,0), (2,0), (1, √3 ) respectively Xcm = (∑ mi xi/∑ mi) ; Ycm = (∑ mi yi/∑ mi) rcm = √X2cm + Y2cm

Q. If three particles of masses 2kg, 1kg and 3 kg are placed at comers of an equilateral triangle of perimeter 6m then the distance of center of mass which is at origin of particles from 1kg mass is (approximately) (Assume 2kg on x-axis )

$6 m$

$2 m$

$\frac{1}{2} m$

2m

Co-ordinates o f 1 kg, 2 kg, 3 kg are (0,0), (2,0), (1, $3$ ) respectively
$X_{c m} = \frac{\sum m _{i} x _{i}}{\sum m _{i}}; Y_{c m} = \frac{\sum m _{i} y _{i}}{\sum m _{i}} r_{c m} = X_{c m}^{2} + Y_{c m}^{2}$

Q. If three particles of masses 2kg, 1kg and 3 kg are placed at comers of an equilateral triangle of perimeter 6m then the distance of center of mass which is at origin of particles from 1kg mass is (approximately) (Assume 2kg on x-axis )

6​m

2​m

2​1​m

2m

Co-ordinates o f 1 kg, 2 kg, 3 kg are (0,0), (2,0), (1, 3​ ) respectively Xcm​=∑mi​∑mi​xi​​;Ycm​=∑mi​∑mi​yi​​rcm​=Xcm2​+Ycm2​​

$6 m$

$2 m$

$\frac{1}{2} m$

Co-ordinates o f 1 kg, 2 kg, 3 kg are (0,0), (2,0), (1, $3$ ) respectively
$X_{c m} = \frac{\sum m _{i} x _{i}}{\sum m _{i}}; Y_{c m} = \frac{\sum m _{i} y _{i}}{\sum m _{i}} r_{c m} = X_{c m}^{2} + Y_{c m}^{2}$