In a one dimensional collision of two particles, velocities are interchanged when: (i) Collision is elastic and masses are equal (ii) Collision is inelastic but masses are unequal Select the correct alternative.

Question

In a one dimensional collision of two particles, velocities are interchanged when: (i) Collision is elastic and masses are equal (ii) Collision is inelastic but masses are unequal Select the correct alternative. (A) only (i) is correct (B) only (ii) is correct (C) both (i) and (ii) are correct (D) both (i) and (ii) are wrong

Tardigrade Admin · Accepted Answer

For elastic collision, v2-v1=u1-u2 ldots ldots (.i.) Momentum conservation, m1u1+m2u2=m1v1+m2u2 For equal masses, u1+u2=v1+v2 ldots ldots (.ii.) Solving (i) (ii) we get, v1=u2 and v2=u1

Q. In a one dimensional collision of two particles, velocities are interchanged when:

(i) Collision is elastic and masses are equal

(ii) Collision is inelastic but masses are unequal

Select the correct alternative.

only (i) is correct

only (ii) is correct

both (i) and (ii) are correct

both (i) and (ii) are wrong

For elastic collision,
$v_{2} - v_{1} = u_{1} - u_{2} \dots\dots (i)$
Momentum conservation,
$m_{1} u_{1} + m_{2} u_{2} = m_{1} v_{1} + m_{2} u_{2}$
For equal masses,
$u_{1} + u_{2} = v_{1} + v_{2} \dots\dots (ii)$
Solving (i) & (ii) we get,
$v_{1} = u_{2}$ and $v_{2} = u_{1}$

Q. In a one dimensional collision of two particles, velocities are interchanged when: (i) Collision is elastic and masses are equal (ii) Collision is inelastic but masses are unequal Select the correct alternative.