If the velocity of a body is doubled, how much should the mass be reduced so that the linear momentum remains the same ? Explain.

1. The momentum of a body is defined as the product of its mass and velocity. Mathematically, $p=mv$, where $p,mandv$ are momentum, mass, and velocity respectively.
2. The total linear momentum in an isolated system remains constant.
3. This implies that the final momentum of the system is equal to the initial momentum of the system. If $p_{1}and{p}_2$ are initial and final momentum of the system respectively then $p_1=p_2$, thus $m_1{v}_1=m_2{v}_2$.
4. Let the initial velocity $\left(v_1\right)$ be $v$ and the mass be $m$ . If the velocity is doubled then the final velocity $\left(v_2\right)$ is $2v$and the mass be $m\text{'}$ .

$mv=m\text{'}\left(2v\right)$

Divide both sides by $2v.$

$\frac{mv}{2v}=\frac{m\text{'}2v}{2v}$

Simplify:

$\frac{m}{2}=m\text{'}orm\text{'}=\frac{m}{2}$

Therefore, if velocity is doubled, the mass should be reduced to half of its initial value.