A smooth sphere of mass M moving with velocity u directly collides elastically with another sphere of mass m at rest. After collision, their final velocities are V and v respectively. The value of v is

Question

A smooth sphere of mass M moving with velocity u directly collides elastically with another sphere of mass m at rest. After collision, their final velocities are V and v respectively. The value of v is (A) (2 u M/m) (B) (2 u m/M) (C) (2 u/1+(m)M) (D) (2 u/1+(M)m)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/a3509deedaad237bfc4d69484f99a119-.png" /> V2 f=((m2-m1/m1+m2)) u2+((2 m1/m1+m2)) u1 Here u1=u, u2=0, m1=M, m2=m, V2 f=v ⇒ v=((2 M/M+m)) u ⇒ v=(2 u/1+(m)M)

Q. A smooth sphere of mass $M$ moving with velocity $u$ directly collides elastically with another sphere of mass $m$ at rest. After collision, their final velocities are $V$ and $v$ respectively. The value of $v$ is

$\frac{2 u M}{m}$

$\frac{2 u m}{M}$

$\frac{2 u}{1 + \frac{m}{M}}$

$\frac{2 u}{1 + \frac{M}{m}}$

$V_{2 f} = (\frac{m _{2} - m _{1}}{m _{1} + m _{2}}) u_{2} + (\frac{2 m _{1}}{m _{1} + m _{2}}) u_{1}$
Here $u_{1} = u, u_{2} = 0, m_{1} = M, m_{2} = m, V_{2 f} = v$
$\Rightarrow v = (\frac{2 M}{M + m}) u$
$\Rightarrow v = \frac{2 u}{1 + \frac{m}{M}}$

Q. A smooth sphere of mass M moving with velocity u directly collides elastically with another sphere of mass m at rest. After collision, their final velocities are V and v respectively. The value of v is

m2uM​

M2um​

1+Mm​2u​

1+mM​2u​