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Units and Dimensions

Two masses ...

Question

Two masses $5 k g$ and $10 k g$ are placed at some distance. If $5 k g$ is moved towards left by $2 m$ and $10 k g$ is moved towards right by $3 m$ . Find the distance by which the center of mass will shift.

A

1.33 m

(Left)

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B

1.33 m

(Right)

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C

1.66 m

(Left)

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D

1.66 m

(Right)

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Solution

The correct option is B $1.33 m$ (Right)
$d x_{c . m} = \frac{m_{1} d x_{1} + m_{2} d x_{2}}{m_{1} + m_{2}}$
$m_{1} = 5 k g$ $d x_{1} = - 2 m$
$m_{2} = 10 k g$ $d x_{2} = + 3 m$

Now,
$d x_{c . m} = \frac{5 \times (- 2) + 10 (3)}{5 + 10}$

$= \frac{- 10 + 30}{15}$
$d x_{c . m} = \frac{20}{15} = + 1.33 m$

(+ve means Right side)

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