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 $