Question

Two masses of 1g and 4 grams are moving with equal Kinetic energies.The ratio of magnitudes of moment A is___ .

Answer 1

The general formula of energy is:
$E_k=\frac{1}{2}m.v^2$
The general formula of momentum:
P = mv
Since the masses are given we only have to equal the energies:
$E_{k1}=E_{k2}$
$\frac{1}{2}.1g.v_1^2=\frac{1}{2}.4g.v_2^2$
$v_1^2=4v_2^2$
$v_1=2v_2$
The momentum of each can be calculated in terms of $v_1$:
$p_1=1.v_1$
$p_2=4.v_2=2.v_1$
And the ratio of the momentum is:
$\frac{p_1}{p_2}=\frac{v_1}{2v_1}=\frac{1}{2}$