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5.work,energy,power and collision — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics5.work,energy,power and collision1 Mark
MCQ
A shell at rest on a smooth horizontal surface explodes into two fragments of masses $m_1$ and $m_2$. If just after explosion $m_1$ move with speed $u$, then work done by internal forces during explosion is
  • A
    $\frac{1}{2}\left(m_1+m_2\right) \frac{m_2}{m_1} u^2$
  • B
    $\frac{1}{2}\left(m_1+m_2\right) u^2$
  • ✓
    $\frac{1}{2} m_1 u^2\left(1+\frac{m_1}{m_2}\right)$
  • D
    $\frac{1}{2}\left(m_2-m_1\right) u^2$
✓

Answer

Correct option: C.
$\frac{1}{2} m_1 u^2\left(1+\frac{m_1}{m_2}\right)$
c
(c)

Using momentum conservation

$m_1 u=m_2 v$

Now using work energy theorem

$W=\frac{P_1^2}{2 m_1}+\frac{P_2^2}{2 m_2}$

$W=\frac{m_1^2 u^2}{2}\left(\frac{m_1+m_2}{m_1 m_2}\right)$

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