A mass of $10 \,gm$ moving with a velocity of $100\, cm/s$ strikes a pendulum bob of mass $10\, gm$. The two masses stick together. The maximum height reached by the system now is ............... $cm$ $(g = 10\,m/{s^2})$
A mass of $10 \,gm$ moving with a velocity of $100\, cm/s$ strikes a pendulum bob of mass $10\, gm$. The two masses stick together. The maximum height reached by the system now is ............... $cm$ $(g = 10\,m/{s^2})$
$0$
$5$
$2.5$
$1.25$
A mass of $10 \,gm$ moving with a velocity of $100\, cm/s$ strikes a pendulum bob of mass $10\, gm$. The two masses stick together. The maximum height reached by the system now is ............... $cm$ $(g = 10\,m/{s^2})$
Initially mass $10 \,gm$ moves with velocity $100 cm/s$
Initial momentum $= 10 × 100$ = $1000\frac{{gm \times m}}{{\sec }}$
After collision system moves with velocity ${v_{{\rm{sys}}{\rm{.}}}}$ then
Final momentum = $(10 + 10) \times {v_{{\rm{sys}}{\rm{.}}}}$
By applying the conservation of momentum
$10000$ = $20 \times {v_{{\rm{sys}}{\rm{.}}}}$==> ${v_{{\rm{sys}}{\rm{.}}}} = = 50\;cm/s$
If system rises upto height $ h$ then
$h = \frac{{v_{{\rm{sys}}{\rm{.}}}^{\rm{2}}}}{{2g}} = \frac{{50 \times 50}}{{2 \times 1000}} = \frac{{2.5}}{2} = 1.25\;cm$