Question

a bomb of mass 10kg is initially at rest explodes into two parts.Mass of 4kg is moving with kinetic energy of 200J.Velocity of other mas is​

Answer 1

Answer:

• Velocity (v) of Other mass is 6.67 m/s.

Given:

1. Total Mass (M) = 10 Kg.
2. Mass of First Body (M₁) = 4 Kg.
3. Kinetic energy of First body (K.E) = 200 J.

Explanation:

$\rule{300}{1.5}$

From Kinetic Energy Formula,

$\large\bigstar \; {\boxed{\tt K.E = \dfrac{1}{2}Mv^2}}$

$\bold{Here}\begin{cases}\sf{M} \; \text{Denotes Mass of Body} \\ \sf{v}\; \text{Denotes Velocity}\end{cases}$

$\large{\boxed{\tt K.E = \dfrac{1}{2}M_1u^2}}$

Substituting the values,

$\large{\tt \longmapsto 200 = \dfrac{1}{2} \times 4 \times (u)^2}$

$\large{\tt \longmapsto 200 \times 2 = 4 \times u^2}$

$\large{\tt \longmapsto 400 = 4 \times u^2}$

$\large{\tt \longmapsto u^2 = \dfrac{400}{4}}$

$\large{\tt \longmapsto u^2 = \cancel{\dfrac{400}{4}}}$

$\large{\tt \longmapsto u^2 = 100}$

$\large{\tt \longmapsto u = \sqrt{100}}$

$\large\longmapsto{\underline{\boxed{\tt u = 10 \: m/s}}}$

$\rule{300}{1.5}$

$\rule{300}{1.5}$

Since, Mass of First body is M₁ = 4 Kg.

Then Mass of Second body is M₂ = 10 Kg - 4 Kg = 6 Kg.

We Know,

From  Law of Conservation of Momentum,

$\large{\boxed{\bold{P_i = P_f}}}$

$\bold{Here}\begin{cases}\sf{P_i} \; \text{Denotes Initial Momentum} \\ \sf{P_f }\; \text{Denotes Final Momentum}\end{cases}$

But Before Exploding The Initial Momentum is Zero.

Substituting,

$\large{\tt \longmapsto P_f = 0}$

$\large{\tt \longmapsto M_1u + M_2v = 0}$

Substituting the values,

$\large{\tt \longmapsto 4 \times 10 + 6 \times u = 0}$

$\large{\tt \longmapsto 40 + 6u = 0}$

$\large{\tt \longmapsto 6u = - 40}$

$\large{\tt \longmapsto u = \dfrac{-40}{6}}$

$\large{\tt \longmapsto u = \cancel{\dfrac{-40}{6}}}$

$\large{\tt \longmapsto u = - 6.67}$

• Here Negative sign indicates that the body is moving opposite direction to the First body.

Taking magnitude,

$\huge{\boxed{\boxed{\tt u = 6.67 \: m/s}}}$

∴ Velocity (v) of Second mass is 6.67 m/s.

$\rule{300}{1.5}$