A body of mass m kg collides elastically with another body at rest and then continues to move in the original direction with one half of its original speed. The mass of the target body is

Question

A body of mass m kg collides elastically with another body at rest and then continues to move in the original direction with one half of its original speed. The mass of the target body is (A) m kg (B) (2/3)m kg (C) (m/3) kg (D) (m/2) kg

Tardigrade Admin · Accepted Answer

Velocity of the colliding body after elastic collision is, v1=u1+(2 m2/m1 + m2)(u2 - u1) (u1/2)=u1+(2 m2/m + m2)(0 - u1) (m2/m + m2)=(1/4) m2=(m/3) kg

Q. A body of mass $m k g$ collides elastically with another body at rest and then continues to move in the original direction with one half of its original speed. The mass of the target body is

$m k g$

$\frac{2}{3} m k g$

$\frac{m}{3} k g$

$\frac{m}{2} k g$

Velocity of the colliding body after elastic collision is,
$v_{1} = u_{1} + \frac{2 m _{2}}{m _{1} + m _{2}} (u_{2} - u_{1})$
$\frac{u _{1}}{2} = u_{1} + \frac{2 m _{2}}{m + m _{2}} (0 - u_{1})$
$\frac{m _{2}}{m + m _{2}} = \frac{1}{4}$
$m_{2} = \frac{m}{3} k g$

Q. A body of mass mkg collides elastically with another body at rest and then continues to move in the original direction with one half of its original speed. The mass of the target body is

mkg

32​mkg

3m​kg

2m​kg