A shell if projected. At some point it explodes in two parts with mass ratio 1:2. The lighter part falls at origin. What is the distance of other part from origin?

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Solution

The correct option is C

The centre of mass will be at the range point = $x_{c m} = (R, 0)$

Position of lighter part of mass (m) = (0 , 0)

Position of greater part of mass (2m) = (x , 0) )

$∴ x_{c m} = \frac{m_{1} x_{1} + m_{2} x_{2}}{m_{1} + m_{2}} \Rightarrow R = \frac{m (0) + 2 m (x)}{3 m}$
$\Rightarrow X = \frac{3 R}{2}$

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A shell if projected. At some point it explodes in two parts with mass ratio 1:2. The lighter part falls at origin. What is the distance of other part from origin?

The correct option is C The centre of mass will be at the range point = xcm=(R,0) Position of lighter part of mass (m) = (0 , 0) Position of greater part of mass (2m) = (x , 0) ) ∴xcm=m1x1+m2x2m1+m2⇒R=m(0)+2m(x)3m ⇒X=3R2