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Q.

A particle of mass 1 g moving with a velocity $\vec{u_{1}} = (3 i - 2 j) {ms}^{- 1}$ experiences a perfectly inelastic collision with another particle of mass 2g and velocity $\vec{u_{2}} = (4 j - 6 k) {ms}^{- 1}$ . The velocity of the combined particle is

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a

i - 3.33 j + 4 k

b

i - 2 j + 4 k

c

i - 2 j - 4 k

d

i + 2 j - 4 k

answer is A.

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Detailed Solution

u_{1} = 3 i - 2 j, u_{2} = 4 j - 6 k

$m_{1} = 1 g, m_{2} = 2g$

$v = \frac{m_{1} u_{1} + m_{2} u_{2}}{m_{1} + m_{2}}$

$\Rightarrow \frac{3 i - 2 j + 2 (4 i - 6 k)}{1 + 2}$

$= \frac{3 i - 2 j + 8 j - 12 k}{3}$

$= \frac{3 i + 6 j - 12 k}{3}$

$= i + 2 j - 4 k$

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A particle of mass 1 g moving with a velocity u1→=(3i−2j)ms−1 experiences a perfectly inelastic collision with another particle of mass 2g and velocity u2→=(4j−6k)ms−1 . The velocity of the combined particle is