Two particles of equal mass m have respective initial velocities and . They collide completely inelastically. The energy lost in the process is

Question

Two particles of equal mass $m$ have respective initial velocities $u \hat{i}$ and $u (\frac{\hat{i} + \hat{j}}{2})$ . They collide completely inelastically. The energy lost in the process is

Smart Achievers · Accepted Answer

(4)

$K_{i} = \frac{1}{2} m (u^{2} + \frac{u^{2}}{2}) = \frac{3}{4} m u^{2}$

$K_{f} = \frac{1}{2} (2 m) \frac{u^{2}}{16} \times 10 = \frac{5}{8} m u^{2}$

$Loss in kinetic energy = \frac{3}{4} m u^{2} - \frac{5}{8} m u^{2} = \frac{1}{8} m u^{2}$

Solution

Q.
Two particles of equal mass $m$ have respective initial velocities $u \hat{i}$ and $u (\frac{\hat{i} + \hat{j}}{2})$ . They collide completely inelastically. The energy lost in the process is

1 $\frac{3}{4} m u^{2}$

2 $\sqrt{\frac{2}{3}} m u^{2}$

3 $\frac{1}{3} m u^{2}$

4 $\frac{1}{8} m u^{2}$

Ans.
(4)

$K_{i} = \frac{1}{2} m (u^{2} + \frac{u^{2}}{2}) = \frac{3}{4} m u^{2}$

$K_{f} = \frac{1}{2} (2 m) \frac{u^{2}}{16} \times 10 = \frac{5}{8} m u^{2}$

$Loss in kinetic energy = \frac{3}{4} m u^{2} - \frac{5}{8} m u^{2} = \frac{1}{8} m u^{2}$

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Solution

Q. Two particles of equal mass m have respective initial velocities ui^ and u(i^+j^2). They collide completely inelastically. The energy lost in the process is

1 34mu2

2 23mu2

3 13mu2

4 18mu2

Ans. (4) Ki=12m(u2+u22)=34mu2 Kf=12(2m)u216×10=58mu2 Loss in kinetic energy =34mu2-58mu2=18mu2