A big ball of mass M, moving with velocity u strikes a small ball of mass m, which is at rest. Finally small ball obtains velocity u and big ball v. Then what is the value of v ?

Question

A big ball of mass M, moving with velocity u strikes a small ball of mass m, which is at rest. Finally small ball obtains velocity u and big ball v. Then what is the value of v ? (A)  (M-m/M)u  (B)  (m/M+m)u  (C)  (2m/M+m)u  (D)  (M/M+m)u

Tardigrade Admin · Accepted Answer

From law of conservation of momentum m1u1+m2u2=m1v1+m2v2 ⇒ Mu+m× 0=Mv+Mu ⇒ v=(M-m/M)u

Q. A big ball of mass $M$ , moving with velocity $u$ strikes a small ball of mass $m$ , which is at rest. Finally small ball obtains velocity $u$ and big ball $v$ . Then what is the value of $v$ ?

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

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

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

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

From law of conservation of momentum
$m_{1} u_{1} + m_{2} u_{2} = m_{1} v_{1} + m_{2} v_{2}$
$\Rightarrow$ $M u + m \times 0 = M v + M u$
$\Rightarrow$ $v = \frac{M - m}{M} u$

Q. A big ball of mass M, moving with velocity u strikes a small ball of mass m, which is at rest. Finally small ball obtains velocity u and big ball v. Then what is the value of v ?

MM−m​u

M+mm​u

M+m2m​u

M+mM​u