# A nucleus splits into two nuclear parts having radii in the ratio 1 : 2. Their velocities are in the ratio

Q. A nucleus splits into two nuclear parts having radii in the ratio 1 : 2. Their velocities are in the ratio

(a) 8 : 1

(b) 6 : 1

(c) 4 : 1

(d) 2 : 1

Ans: (a)

Sol: Applying conservation of momentum ,

m1v1 = m2v2

$\displaystyle \rho \frac{4}{3}\pi r_1^3 v_1 = \rho \frac{4}{3}\pi r_2^3 v_2$

$\displaystyle r_1^3 v_1 = r_2^3 v_2$

$\displaystyle \frac{v_1}{v_2} = (\frac{r_2}{r_1})^3 = (2)^3$

$\displaystyle \frac{v_1}{v_2} = 8$