NEET
- Exam
- NEET
- Subject
- Physics
- Chapter
- Center of Mass, Momentum and Collision
NEET · Physics · Center of Mass, Momentum and Collision
Two particles mass m_1 and m_2 are kept at rest at t=0 . They start...
Two particles mass and are kept at rest at . They start attracting each other due to their gravitational pull, then
Statement-I: The total momentum of the system is zero at any instant.
Statement-II: Both the particles gain equal momentum in opposite direction in equal interval of time as both are acted upon equal and opposite forces.
Options
- ABoth Statement-I and Statement-II are correct.
- BBoth Statement-I and Statement-II are incorrect.
- CStatement-I is correct and Statement-II is incorrect.
- DStatement-I is incorrect and Statement-II is correct.
Correct answer
A. Both Statement-I and Statement-II are correct.
Step-by-step solution
1. By Newton's third law the internal forces are equal and opposite:
(\mathrm{F}_{12}=-\mathrm{F}_{21} .)
If (\mathrm{p}_1, \mathrm{p}_2) are momenta, then
(\frac{d \mathrm{p}_1}{d t}=\mathrm{F}_{12}, \quad \frac{d \mathrm{p}_2}{d t}=\mathrm{F}_{21}=-\mathrm{F}_{12} .)
Add them:
(\frac{d}{d t}\left(\mathrm{p}_1+\mathrm{p}_2\right)=0 \Rightarrow \mathrm{p}_1+\mathrm{p}_2=\text{ constant })
Initially both particles are at rest, so (\mathrm{p}_1+\mathrm{p}_2=\mathrm{0}). Hence at every later time the total momentum remains zero. This proves Statement I.
2. From the pair of equations above,
(\frac{d \mathrm{p}_1}{d t}=-\frac{d \mathrm{p}_2}{d t} .)
Integrating over any equal time interval gives
(\Delta \mathrm{p}_1=-\Delta \mathrm{p}_2,)
i.e. they gain equal magnitude momenta in opposite directions (even though their velocities will be different if (m_1 \neq m_2)). That proves Statement II.
Both statements are therefore true (and Statement II (\downarrow) ist the differential form of the same Newton-third law fact that ensures Statement J).