On a horizontal smooth surface,a disc of radi | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the radius of the incoming disc be $r_2$. The impact parameter $b$ is given as $r_2$.For two discs of radii $r$ and $r_2$,the impact parameter

Vedclass · Accepted Answer

$\frac{r}{\sqrt{2}-1}$

Vedclass · Answer

(C) Let the radius of the incoming disc be $r_2$. The impact parameter $b$ is given as $r_2$.For two discs of radii $r$ and $r_2$,the impact parameter $b$ is related to the scattering angle $	heta$ by the geometry of the collision.The line connecting the centers of the discs at the moment of impact makes an angle $\phi$ with the direction of the incoming disc,where $\sin \phi = \frac{b}{r+r_2}$.Given $b = r_2$,we have $\sin \phi = \frac{r_2}{r+r_2}$.For equal masses,the velocity vectors after collision are perpendicular if the collision is elastic. However,the scattering angle of the target disc is determined by the geometry of the impact.Given the target disc moves at $45^{\circ}$,the geometry implies $\phi = 45^{\circ}$.Thus,$\sin 45^{\circ} = \frac{r_2}{r+r_2}$.$\frac{1}{\sqrt{2}} = \frac{r_2}{r+r_2}$.$r+r_2 = \sqrt{2} r_2$.$r = r_2(\sqrt{2}-1)$.$r_2 = \frac{r}{\sqrt{2}-1}$.

Similar Questions

When two particles collide elastically,then impulsive force can't change

The bob of a simple pendulum (mass $m$ and length $l$) is dropped from a horizontal position. It strikes a block of the same mass $m$ placed on a horizontal frictionless table. The collision is elastic. The kinetic energy of the block after the collision will be

Object $A$ moving with velocity $v$ on a straight line collides with a stationary object $B$. After the collision,$B$ attains a velocity of $1.6v$. Assuming the collision is perfectly elastic,what percentage of $A$'s energy is transferred to $B$ during the collision?

Three blocks are initially placed as shown in the figure. Block $A$ has mass $m$ and initial velocity $v$ to the right. Block $B$ with mass $m$ and block $C$ with mass $4m$ are both initially at rest. Neglect friction. All collisions are elastic. The final velocity of block $A$ is

$A$ neutron travelling with a velocity $v$ and kinetic energy $E$ collides perfectly elastically head-on with the nucleus of an atom of mass number $A$ at rest. The fraction of total energy retained by the neutron is

Vedclass Test Series

Exam Paper Generator

Online Exam Module