Question 291: Centre of Mass and Rotational Motion

Question

A ball with a speed of 9 m/s collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of 30$$^\circ$$ with the original direction. The ratio of velocities of the balls after collision is x : y, where x is __________.

Accepted Answer

The situation is shown below
Using conservation of linear momentum in y-direction,
p
i
= p
f
As, p
i
= 0
and p
f
= mv
1
sin30$$^\circ$$ $$-$$ mv
2
sin30$$^\circ$$
$$\Rightarrow$$ 0 = m $$	imes$$ $${1 \over 2}$$v
1
$$-$$ m $$	imes$$ $${1 \over 2}$$v
2
$$\Rightarrow$$ v
1
= v
2
or v
1
: v
2
= 1 : 1
Since, v
1
: v
2
= x : y (given)
$$	herefore$$ x = 1

Centre of Mass and Rotational Motion

A ball with a speed of 9 m/s collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of 30$^\circ$ with the original direction. The ratio of velocities of the balls after collision is x : y, where x is __________.

Integer / Numeric Answer Type