A sphere of mass m moving with constant velocity μ , collides with another stationary sphere of same mass. If e is the coefficient of restitution, the ratio of the final velocities of the first and second spheres is

Question

A sphere of mass m moving with constant velocity μ , collides with another stationary sphere of same mass. If e is the coefficient of restitution, the ratio of the final velocities of the first and second spheres is (A)  (1+e/1-e)  (B)  (1-e/1+e)  (C)  (e/1-e)  (D)  (1+e/e)

Tardigrade Admin · Accepted Answer

Let v1,v2 be the final velocities of the two spheres. Applying the law of conservation of linear momentum mu=m(v1+v2) or v1+v2=u ?(i) Again the coefficient of restitution is given by e=(v2-v1/u) or v2-v1=eu ?(ii) Solving Eqs. (i) and (ii), we get v1=(u/2)(1-e),v2=(u/2)(1+e) Therefore, (v1/v2)=( (1-e/1+e) )

Q. A sphere of mass m moving with constant velocity $μ$ , collides with another stationary sphere of same mass. If e is the coefficient of restitution, the ratio of the final velocities of the first and second spheres is

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

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

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

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

Q. A sphere of mass m moving with constant velocity μ , collides with another stationary sphere of same mass. If e is the coefficient of restitution, the ratio of the final velocities of the first and second spheres is

1−e1+e​

1+e1−e​

1−ee​

e1+e​

Q. A sphere of mass m moving with constant velocity $μ$ , collides with another stationary sphere of same mass. If e is the coefficient of restitution, the ratio of the final velocities of the first and second spheres is

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

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

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

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