A sphere S1 impings directly on an equal sphere S2 at rest. If the coefficient of restitution is e , then the velocities of S1 and S2 are in the ratio

Question

A sphere S1 impings directly on an equal sphere S2 at rest. If the coefficient of restitution is e , then the velocities of S1 and S2 are in the ratio (A)  (1+e/1-e)  (B)  (1-e/1+e)  (C)  (e-1/e+1)  (D)  (e+1/e-1)

Tardigrade Admin · Accepted Answer

Let m be the mass of each sphere. Let u be the velocity of the first sphere before impact and v1 and v2 be their velocities after impact, then v1-v2=-e u ....(i) and m v1+m v2=m u ⇒ v1+v2=u ....(ii) On solving Eqs. (i) and (ii), we get v1=(u(1-e)/2) and v2=(u(1+e)/2) ∴ (v1/v2)=(1-e/1+e)

Q. $A$ sphere $S_{1}$ impings directly on an equal sphere $S_{2}$ at rest. If the coefficient of restitution is $e$ , then the velocities of $S_{1}$ and $S_{2}$ are in the ratio

$\frac{1 + e}{1 - e}$

$\frac{1 - e}{1 + e}$

$\frac{e - 1}{e + 1}$

$\frac{e + 1}{e - 1}$

Q. A sphere S1​ impings directly on an equal sphere S2​ at rest. If the coefficient of restitution is e , then the velocities of S1​ and S2​ are in the ratio

1−e1+e​

1+e1−e​

e+1e−1​

e−1e+1​

Q. $A$ sphere $S_{1}$ impings directly on an equal sphere $S_{2}$ at rest. If the coefficient of restitution is $e$ , then the velocities of $S_{1}$ and $S_{2}$ are in the ratio

$\frac{1 + e}{1 - e}$

$\frac{1 - e}{1 + e}$

$\frac{e - 1}{e + 1}$

$\frac{e + 1}{e - 1}$