Question

Which of the following is true for center of mass?
$\left(i\right)$ The center of mass of a body may lie within, outside, on the surface of the body.

$\left(ii\right)$ In the case of symmetrical bodies, the center of mass coincides with the geometrical center of the body.

$\left(iii\right)$ In the absence of external forces, the center of mass moves with constant velocity.

$\left(iv\right)$ If external forces are absent and system is initially at rest, then location of center of mass is fixed.

• A. $\left(ii\right),\left(iii\right),\left(iv\right)$
• B. $\left(i\right),\left(ii\right),\left(iii\right)$
• C. $\text{all option are correct}$
• D. $\left(i\right),\left(ii\right)$

Answer 1

The correct option is C $\text{all option are correct}$

$\left(i\right)$ If we take unsymmetrical shaped body then centre of mass can lies within or surface of the body.
But if we take $L-\text{shaped}$ body or ring then centre of mass will lie outside the body.

$\left(ii\right)$ If we take body which is symmetrical in shape like sphere, square etc. then its centre of mass will be at its geometrical centre.

$\left(iii\right)$ If $F_{ext}=0$
Then $a_{cm}=0$
$\Rightarrow v_{cm}=\text{constant}$

$\left(iv\right)$If initially system is at rest, $v_{cm}=0$
And $F_{ext}=0$
Then centre of mass will not change its position.