Q152 / 160 · AP EAMCET 2020 (18 Sep Shift 2) · Physics

A bomb at rest explodes into three parts of equal mass. If the momentum of two parts are \(-2 p \hat{\mathbf{i}}\) and \(p \hat{\mathbf{j}}\), find the magnitude of momentum of the third part.

  • A
    \(p\)
  • B
    \(\sqrt{3} p\)
  • Correct answer
    C
    \(\sqrt{5} p\)
  • D
    0

Solution

If \(p^{\prime} \hat{\mathbf{n}}\) be the momentum of third parts, then according to conservation of linear momentum. Total moment before explosion \(=\) Total momentum after explosion \(\begin{array}{lll} & \Rightarrow 0 =-2 p \hat{\mathbf{i}}+p \hat{\mathbf{j}}+p^{\prime} \hat{\mathbf{n}} \\ & \Rightarrow p^{\prime} \hat{\mathbf{n}} =2 p \hat{\mathbf{i}}-p \hat{\mathbf{j}} \\ & \therefore \text {Magnitude of } p^{\prime} \hat{\mathbf{n}}=p^{\prime} \\ & =\sqrt{(2 p)^2+(-p)^2}=\sqrt{5 p^2}=\sqrt{5 p} \end{array}\)

Hence, the correct answer is option: 'C'.

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