Question

Two mass of $1g$ and $4g$ are moving with kinetic energy in the ratio $4:1.$ What is the ratio of their linear momentum?

• A. $6:1$
• B. $4:1$
• C. $1:2$
• D. $1:1$

Answer 1

The correct option is D $1:1$

Given:
$m_1=1g$ and $m_2=4g$
$E_1$ and $E_2$ be the kinetic energies of the two masses.

$\frac{E_1}{E_2}=\frac{4}{1}$ .........given

$v_1$ and $v_2$ be the velocities of the two masses,
$p_1$ and $p_2$ be the momenta of the two masses,
Now, we know

$\frac{E_1}{E_2}=\frac{m_1{v_1}^2}{m_2{v_2}^2}$

$\Rightarrow \frac{m_1{v_1}^2}{m_2{v_2}^2}=\frac{4}{1}$

$\Rightarrow \frac{1}{4}\times \frac{{v_1}^2}{{v_2}^2}=\frac{4}{1}$

$\Rightarrow \frac{{v_1}^2}{{v_2}^2}=\frac{16}{1}$

$\Rightarrow \frac{v_1}{v_2}=\frac{4}{1}$

$\Rightarrow \frac{m_1{v}_1}{m_2{v}_2}=\frac{1\times 4}{4\times 1}$

$\Rightarrow \frac{p_1}{p_2}=\frac{1}{1}$