Two homogeneous spheres A and B of masses m and 2m having radii 2a and a respectively are placed in touch. The distance of the centre of mass from the centre of the first sphere is

Question

Two homogeneous spheres A and B of masses m and 2m having radii 2a and a respectively are placed in touch. The distance of the centre of mass from the centre of the first sphere is (A) a (B) 2a (C) 3a (D) none of these

Tardigrade Admin · Accepted Answer

We assume that origin is situated at O1 . <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-23r7vow0jki0bbil.jpg" /> ∴ x1=0 , m1=m x2=3a , m2=2m ∴ xcm=(m1 x1 + m2 x2/m1 + m2) =((m × 0) + (2 m × 3 a)/m + 2 m) =(6 ma/3 m)=2a

Q. Two homogeneous spheres $A$ and $B$ of masses $m$ and $2 m$ having radii $2 a$ and $a$ respectively are placed in touch. The distance of the centre of mass from the centre of the first sphere is

$a$

$2 a$

$3 a$

none of these

We assume that origin is situated at $O_{1}$ .

$∴ x_{1} = 0$ , $m_{1} = m$
$x_{2} = 3 a$ , $m_{2} = 2 m$
$∴ x_{c m} = \frac{m _{1} x _{1} + m _{2} x _{2}}{m _{1} + m _{2}}$
$= \frac{( m \times 0 ) + ( 2 m \times 3 a )}{m + 2 m}$
$= \frac{6 ma}{3 m} = 2 a$

Q. Two homogeneous spheres A and B of masses m and 2m having radii 2a and a respectively are placed in touch. The distance of the centre of mass from the centre of the first sphere is

a

2a

3a

none of these

We assume that origin is situated at O1​ . ∴x1​=0 , m1​=m x2​=3a , m2​=2m ∴xcm​=m1​+m2​m1​x1​+m2​x2​​ =m+2m(m×0)+(2m×3a)​ =3m6ma​=2a

Q. Two homogeneous spheres $A$ and $B$ of masses $m$ and $2 m$ having radii $2 a$ and $a$ respectively are placed in touch. The distance of the centre of mass from the centre of the first sphere is

$a$

$2 a$

$3 a$

We assume that origin is situated at $O_{1}$ .

$∴ x_{1} = 0$ , $m_{1} = m$
$x_{2} = 3 a$ , $m_{2} = 2 m$
$∴ x_{c m} = \frac{m _{1} x _{1} + m _{2} x _{2}}{m _{1} + m _{2}}$
$= \frac{( m \times 0 ) + ( 2 m \times 3 a )}{m + 2 m}$
$= \frac{6 ma}{3 m} = 2 a$