Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# Consider the Following Two Statements: (A) Linear Momentum of a System of Particles is Zero. (B) Kinetic Energy of a System of Particles is Zero. - Physics

MCQ

Consider the following two statements:

(A) Linear momentum of a system of particles is zero.

(B) Kinetic energy of a system of particles is zero.

#### Options

• A implies B and B implies A.

• A does not imply B and B does not imply A.

• A implies B but B does not imply A.

• B implies A but A does not imply B.

#### Solution

B implies A but A does not imply B.

If the linear momentum of a system is zero,
$\Rightarrow m_1 \vec{v}_1 + m_2 \vec{v}_2 + . . .$ =0
Thus, for a system of comprising two particles of same masses,
$\vec{v}_1 = - \vec{v}_2$    ...(1)
The kinetic energy of the system is given by,
$K . E . = \frac{1}{2}m \vec{v}_1^2 + \frac{1}{2}m \vec{v}_2^2$
Using equation (1) to solve above equation, we can say:
$K . E . \neq 0$

i.e A does not imply B .
Now,
If the kinetic energy of the system is zero,
$\Rightarrow \frac{1}{2}m \vec{v}_1^2 + \frac{1}{2}m \vec{v}_2^2 = 0$
$v_1 = \pm v_2$
On calculating the linear momentum of the system, we get:
$\vec{P} = m \vec{v}_1 + m \vec{v}_2$
$\text{ taking v_1 = - v_2 , we can write:}$
$\vec{P} = 0$

Hence, we can say, B implies A but A does not imply B.

Concept: Momentum Conservation and Centre of Mass Motion
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#### APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 9 Centre of Mass, Linear Momentum, Collision
MCQ | Q 3 | Page 157