A body of mass m1 moving with an unknown velocity of v1 hati, undergoes a collinear collision with a body of mass m2 moving with a velocity v2 hati . After collision, m1 and m2 move with velocities of v3 hati and v4 hati , respectively. If m2 = 0.5 m1 and v3 = 0.5 v1 , then v1 is :-

Question

A body of mass m1 moving with an unknown velocity of v1 hati, undergoes a collinear collision with a body of mass m2 moving with a velocity v2 hati . After collision, m1 and m2 move with velocities of v3 hati and v4 hati , respectively. If m2 = 0.5 m1 and v3 = 0.5 v1 , then v1 is :- (A) v4 - (v2/4) (B) v4 - (v2/2) (C) v4 - v2 (D) v4 + v2

Tardigrade Admin · Accepted Answer

Applying linear momentum conservation m1v1 hati + m2 v2 hati = m1 v3 hati +m2 v4 hati m1v1 + 0.5 m1v2 = m1(0.5v1) + 0.5 m1v4 0.5 m1v1 = 0.5 m1 (v4-v2) v1 =v4 -v2

$v_{4} - \frac{v _{2}}{4}$

$v_{4} - \frac{v _{2}}{2}$

$v_{4} - v_{2}$

$v_{4} + v_{2}$

Applying linear momentum conservation $m_{1} v_{1} \hat{i} + m_{2} v_{2} \hat{i} = m_{1} v_{3} \hat{i} + m_{2} v_{4} \hat{i}$
$m_{1} v_{1} + 0.5 m_{1} v_{2} = m_{1} (0.5 v_{1}) + 0.5 m_{1} v_{4}$
$0.5 m_{1} v_{1} = 0.5 m_{1} (v_{4} - v_{2})$
$v_{1} = v_{4} - v_{2}$

v4​−4v2​​

v4​−2v2​​

v4​−v2​

v4​+v2​

Applying linear momentum conservation m1​v1​i^+m2​v2​i^=m1​v3​i^+m2​v4​i^ m1​v1​+0.5m1​v2​=m1​(0.5v1​)+0.5m1​v4​ 0.5m1​v1​=0.5m1​(v4​−v2​) v1​=v4​−v2​

$v_{4} - \frac{v _{2}}{4}$

$v_{4} - \frac{v _{2}}{2}$

$v_{4} - v_{2}$

$v_{4} + v_{2}$

Applying linear momentum conservation $m_{1} v_{1} \hat{i} + m_{2} v_{2} \hat{i} = m_{1} v_{3} \hat{i} + m_{2} v_{4} \hat{i}$
$m_{1} v_{1} + 0.5 m_{1} v_{2} = m_{1} (0.5 v_{1}) + 0.5 m_{1} v_{4}$
$0.5 m_{1} v_{1} = 0.5 m_{1} (v_{4} - v_{2})$
$v_{1} = v_{4} - v_{2}$