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PART - 1 CH - 4 Laws of Motion — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsPART - 1 CH - 4 Laws of Motion2 Marks
Question
A sphere of mass $m kg$ moving with velocity $v$ stops after sinking into a hanging sand bag. If the mass of sand bag is $M$ and it rises to a height of $h$ then find the velocity of sphere.
✓

Answer

According to law of conservation of momentum
$m V=(M+m) v \ \ldots(1)$
Image
Here V is velocity of sphere and $v$ is common velocity of sand bag and sphere after hitting. After the collision the bag and sphere both rises to a height $h$ then according to law of conservation of energy,
$\begin{array}{rlrl}
\frac{1}{2}(M+m) v^2 & =(M+m) g h \ \ldots(2) \\
\Rightarrow \quad v^2 & =2 g h
\end{array}$
From equation (1)
$m V=( M +m) \sqrt{2 g h}$
$\therefore \quad V=\left(\frac{M+m}{m}\right) \sqrt{2 g h}\quad \text { Ans. }$

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