Lf all the particles of a system lie in X-Y plane- is it necessary that the centre of mass be in X-Y plane- Never-Some times-Not theoretically but practically-Yes-

The correct option is D Yes We know for the system of point particles, x_COM = m_1x_1 + m_2x_2 + .../m_1 + m_2 +... y_COM = m_1y_1 + m_2y_2 + .../m_1 + m_2 +.. ...

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Byju's Answer

Standard IX

Physics

Intuition for COM

lf all the pa...

Question

lf all the particles of a system lie in X-Y plane, is it necessary that the centre of mass be in X-Y plane?

Yes

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Never

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Some times

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Not theoretically but practically

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Solution

The correct option is A
Yes

We know for the system of point particles,

$x_{C O M} = \frac{m_{1} x_{1} + m_{2} x_{2} + . . .}{m_{1} + m_{2} + . . .}$
$y_{C O M} = \frac{m_{1} y_{1} + m_{2} y_{2} + . . .}{m_{1} + m_{2} + . . .}$
$z_{C O M} = \frac{m_{1} z_{1} + m_{2} z_{2} + . . .}{m_{1} + m_{2} + . . .}$
If all particles are in x - y plane
$\Rightarrow z_{1} = z_{2} = z_{3} = 0$
$\Rightarrow$ COM will also lie in x - y plane.

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Similar questions

Q. If all the particle of a system lie in a cube, is it necessary that the centre of mass be in the cube?

Q. The centre of mass is defined as

\vec{R} = \frac{1}{M} \sum_{i} m_{i} \vec{r_{i}}

. Suppose we define "centre of charge" as

{\vec{R}}_{c} = \frac{1}{Q} \sum_{i} q_{i} \vec{r_{i}}

where q_i represents the ith charge placed at

{\vec{r}}_{i}

and Q is the total charge of the system.
(a) Can the centre of charge of a two-charge system be outside the line segment joining the charges?
(b) If all the charges of a system are in X-Y plane, is it necessary that the centre of charge be in X-Y plane?
(c) If all the charges of a system lie in a cube, is it necessary that the centre of charge be in the cube?

lf all the particles of a system lie in X-Y plane, is it necessary that the centre of mass be in X-Y plane?

Q. If all the particles of a system lie in X-Y plane, is it necessary that the centre of mass be in X-Y plane?

lf all the particles of a system lie in a cube, is it necessary that the centre of mass be in the cube?

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lf all the particles of a system lie in X-Y plane, is it necessary that the centre of mass be in X-Y plane?

The correct option is A Yes We know for the system of point particles, xCOM = m1x1 + m2x2 + ...m1 + m2 +... yCOM = m1y1 + m2y2 + ...m1 + m2 +... zCOM = m1z1 + m2z2 + ...m1 + m2 +... If all particles are in x - y plane ⇒ z1 = z2 = z3 = 0 ⇒ COM will also lie in x - y plane.