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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Never

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Some times

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Not theoretically but practically

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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.

Suggest Corrections

Similar questions

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?

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

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?

The sphere shown in figure lies on a rough plane when a particle of mass m travelling at a speed v0 collides and sticks with it. If the line of motion of the particle is at a distance h above the plane, find the linear speed of the combined system just after the collision. Assume that the mass M of the sphere is large compared to the mass of the particle so that the centre of mass of the combined system is not appreciably shifted from the centre of the sphere.

Join BYJU'S Learning Program

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.