1 \(\frac{{2\,\mu {M^2}g}}{{{p^2}}}\)
2 \(\frac{p}{{2\,\mu Mg}}\)
3 \(\frac{{2\,\mu Mg}}{p}\)
4 \(\frac{{{p^2}}}{{2\,\mu {M^2}g}}\)
Explanation:
Using kinematic relation
\({v^2} = {u^2} - 2as\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\)
If the speed of the block is \(u\) the momentum \(p\) is given by
\(p = Mu\)
\(u = \frac{p}{M}\) and deceleration is given as
\(a = \mu g\)
substituting values in eq.(1), we get
\(0 = {u^2} - 2as\) (\(\because \) final velocity, \(v = 0\))
\( \Rightarrow 0 = {\left( {\frac{p}{M}} \right)^2} - 2\mu gs\)
\( \Rightarrow s = \frac{{{p^2}}}{{2{M^2}\mu g}}\)
