Question 279: Centre of Mass and Rotational Motion

Question

A ball of mass 10 kg moving with a velocity 10$$\sqrt 3 $$ m/s along the x-axis, hits another ball of mass 20 kg which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along y-axis with a speed of 10 m/s. The second piece starts moving at an angle of 30$$^\circ$$ with respect to the x-axis. The velocity of the ball moving at 30$$^\circ$$ with x-axis is x m/s. The configuration of pieces after collision is shown in the figure below. The value of x to the nearest integer is ____________.

Accepted Answer

Velocity of 10 kg ball = $${v_{10}} = 10\sqrt {3\widehat i} $$
initial total momentum of system = $$10 	imes 10\sqrt {3\widehat i} $$
Final total momentum of system
$$ = 10 	imes 10\widehat j + 10 	imes x(\cos 30^\circ \widehat i - \sin 30^\circ \widehat j)$$
Now by conservation of momentum
$$10 	imes 10\sqrt {3\widehat i}  = 10 	imes 10\widehat j + 10 	imes x\left( {{{\sqrt 3 } \over 2}\widehat i - {1 \over 2}\widehat j} ight)$$
$$ \Rightarrow $$ x = 20

Centre of Mass and Rotational Motion

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