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An object of mass $M$ is at the origin and is at rest. Suddenly an explosion happens in the object and object is divided three equal parts.
The first part goes with the velocity $\left(v_0 \mathrm{i}+\mathrm{v}_0 \mathrm{j}\right)$.
The second part goes with the velocity $\mathrm{v}_0 \mathrm{j}$
What is the velocity vector for the third part?
Options:
The first part goes with the velocity $\left(v_0 \mathrm{i}+\mathrm{v}_0 \mathrm{j}\right)$.
The second part goes with the velocity $\mathrm{v}_0 \mathrm{j}$
What is the velocity vector for the third part?
Solution:
1443 Upvotes
Verified Answer
The correct answer is:
$\left(-v_0 i-2 v_0 j\right)$
Applying law of conservation of linear momentum
$\mathbf{0}=\frac{M}{3}\left(v_0 \mathbf{i}+v_0 \mathbf{j}\right)+\frac{M}{3}\left(v_0 \mathbf{j}\right)+\frac{M}{3} \mathbf{v}$
Or
$\mathbf{v}=-v_0 \mathbf{i}-2 v_0 \mathbf{j}$
$\mathbf{0}=\frac{M}{3}\left(v_0 \mathbf{i}+v_0 \mathbf{j}\right)+\frac{M}{3}\left(v_0 \mathbf{j}\right)+\frac{M}{3} \mathbf{v}$
Or
$\mathbf{v}=-v_0 \mathbf{i}-2 v_0 \mathbf{j}$
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