Masses of 2 kg each are placed at the corners B and A of a rectangular plate A B C D as shown in the figure. A mass of 8 kg has to be placed on the plate so that the centre of mass of the system should be the centre O. Then the mass should be placed at:

Question

Masses of 2 kg each are placed at the corners B and A of a rectangular plate A B C D as shown in the figure. A mass of 8 kg has to be placed on the plate so that the centre of mass of the system should be the centre O. Then the mass should be placed at: (A) 1m from O on OE (B) 2m from O on OF (C) 2m from O on OG (D) 2m from O on OH

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/c8065c8565359209da2cbe92b0a3c19b-.png" /> x cm =(m1 x1+m2 x2+m3 x3/m1+m2+m3) ⇒ 0=(2(-2)+2(-2)+8 x3/2+2+8) ⇒ x3=1 m

Q. Masses of $2 k g$ each are placed at the corners $B$ and $A$ of a rectangular plate $A BC D$ as shown in the figure. A mass of $8 k g$ has to be placed on the plate so that the centre of mass of the system should be the centre O. Then the mass should be placed at:

1m from O on OE

2m from O on OF

2m from O on OG

2m from O on OH

$x_{c m} = \frac{m _{1} x _{1} + m _{2} x _{2} + m _{3} x _{3}}{m _{1} + m _{2} + m _{3}}$
$\Rightarrow 0 = \frac{2 ( - 2 ) + 2 ( - 2 ) + 8 x _{3}}{2 + 2 + 8}$
$\Rightarrow x_{3} = 1 m$

Q. Masses of 2kg each are placed at the corners B and A of a rectangular plate ABCD as shown in the figure. A mass of 8kg has to be placed on the plate so that the centre of mass of the system should be the centre O. Then the mass should be placed at: