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Q.

A 500kg automobile is moving along a straight high way at $10 {ms}^{- 1}$ . Another car with mass 1000kg and speed $30 {ms}^{- 1}$ is 30m ahead of first. Then velocity of CM is

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a

14.2 {ms}^{- 1}

b

23.3 {ms}^{- 1}

c

15 {ms}^{- 1}

d

18.5 {ms}^{- 1}

answer is B.

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Detailed Solution

Given

m_{1} = 500 {kg,  v}_{1} = 10 m/s

$m_{2} = 1000 {kg, v}_{2} = 30 m/s$

${\vec{v}}_{c m} = \frac{m_{1} {\vec{v}}_{1} + m_{2} {\vec{v}}_{2}}{m_{1} + m_{2}}$

$= \frac{500 (10) + 1000 (30)}{500 + 1000}$

$= \frac{5000 + 30000}{1500} = \frac{35000}{1500}$

$= 23.3 m/s$

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A 500kg automobile is moving along a straight high way at10 ms−1 . Another car with mass 1000kg and speed 30 ms−1 is 30m ahead of first. Then velocity of CM is