Two small particles of equal masses start moving in opposite directions from a point $A$ in a horizontal circular orbit. Their tangential velocities are $v$ and $2 v$, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at $A$, these two particles will again reach the point $A$ ?
Two small particles of equal masses start moving in opposite directions from a point $A$ in a horizontal circular orbit. Their tangential velocities are $v$ and $2 v$, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at $A$, these two particles will again reach the point $A$ ?
- [IIT 2009]
- A
$4$
- B
$3$
- C
$2$
- D
$1$
Similar Questions
A point mass of $1 \mathrm{~kg}$ collides elastically with a stationary point mass of $5 \mathrm{~kg}$. After their collision, the $1 \mathrm{~kg}$ mass reverses its direction and moves with a speed of $2 \mathrm{~ms}^{-1}$. Which of the following statement(s) is (are) correct for the system of these two masses?
$(A)$ Total momentum of the system is $3 \mathrm{~kg} \mathrm{~ms}^{-1}$
$(B)$ Momentum of $5 \mathrm{~kg}$ mass after collision is $4 \mathrm{~kg} \mathrm{~ms}^{-1}$
$(C)$ Kinetic energy of the centre of mass is $0.75 \mathrm{~J}$
$(D)$ Total kinetic energy of the system is $4 \mathrm{~J}$
A point mass of $1 \mathrm{~kg}$ collides elastically with a stationary point mass of $5 \mathrm{~kg}$. After their collision, the $1 \mathrm{~kg}$ mass reverses its direction and moves with a speed of $2 \mathrm{~ms}^{-1}$. Which of the following statement(s) is (are) correct for the system of these two masses?
$(A)$ Total momentum of the system is $3 \mathrm{~kg} \mathrm{~ms}^{-1}$
$(B)$ Momentum of $5 \mathrm{~kg}$ mass after collision is $4 \mathrm{~kg} \mathrm{~ms}^{-1}$
$(C)$ Kinetic energy of the centre of mass is $0.75 \mathrm{~J}$
$(D)$ Total kinetic energy of the system is $4 \mathrm{~J}$
- [IIT 2010]
A particle falls from a height $h $ upon a fixed horizontal plane and rebounds. If $e$ is the coefficient of restitution, the total distance travelled before rebounding has stopped is
A particle falls from a height $h $ upon a fixed horizontal plane and rebounds. If $e$ is the coefficient of restitution, the total distance travelled before rebounding has stopped is
$Assertion$ : If collision occurs between two elastic bodies their kinetic energy decreases during the time of collision.
$Reason$ : During collision intermolecular space decreases and hence elastic potential energy increases.
$Assertion$ : If collision occurs between two elastic bodies their kinetic energy decreases during the time of collision.
$Reason$ : During collision intermolecular space decreases and hence elastic potential energy increases.
- [AIIMS 2015]
A ball of mass $200\,g$ rests on a vertical post of height $20\,m$. A bullet of mass $10\,g$, travelling in horizontal direction, hits the centre of the ball. After collision both travels independently. The ball hits the ground at a distance $30\,m$ and the bullet at a distance of $120\,m$ from the foot of the post. The value of initial velocity of the bullet will be $............m/s$ (if $\left.g =10 m / s ^2\right)$
A ball of mass $200\,g$ rests on a vertical post of height $20\,m$. A bullet of mass $10\,g$, travelling in horizontal direction, hits the centre of the ball. After collision both travels independently. The ball hits the ground at a distance $30\,m$ and the bullet at a distance of $120\,m$ from the foot of the post. The value of initial velocity of the bullet will be $............m/s$ (if $\left.g =10 m / s ^2\right)$
- [JEE MAIN 2023]
Two balls in free space are colliding with each other. Which of the following statement regarding linear momentum conservation of the system is true ?
Two balls in free space are colliding with each other. Which of the following statement regarding linear momentum conservation of the system is true ?