Question 149: Centre of Mass and Rotational Motion

Question

Two particles of equal mass m have respective
initial velocities $$u\widehat i$$ and $$u\left( {{{\widehat i + \widehat j} \over 2}} \right)$$.
They collide
completely inelastically. The energy lost in the
process is :

Accepted Answer

$$\overrightarrow {{P_i}}  = \overrightarrow {{P_f}} $$
$$ \Rightarrow $$ mu$$\widehat i$$ + m$$\left( {{u \over 2}\widehat i + {u \over 2}\widehat j} ight)$$ = 2m$$\overrightarrow v $$
Compare both side
$$\overrightarrow v  = $$ $${{3u} \over 4}\widehat i + {u \over 4}\widehat j$$
$$ \Rightarrow $$ $${\left| {\overrightarrow v } ight|^2}$$ = $${{10{u^2}} \over {16}}$$
$$\Delta $$KE = KE
f
Ã¢ÂÂ KE
i
= $${1 \over 2}2m 	imes {{10{u^2}} \over {16}}$$ - $${1 \over 2}m{u^2}$$ - $${1 \over 2}m{\left( {{u \over {\sqrt 2 }}} ight)^2}$$
= $$ - {1 \over 8}m{u^2}$$

Answer

$${1 \over 3}m{u^2}$$

Answer

$${1 \over 8}m{u^2}$$

Answer

$${3 \over 4}m{u^2}$$

Answer

$$\sqrt {{2 \over 3}} m{u^2}$$

Centre of Mass and Rotational Motion

Two particles of equal mass m have respective initial velocities $u\widehat i and u\left( {{{\widehat i + \widehat j} \over 2}} \right)$. They collide completely inelastically. The energy lost in the process is :

Choose the correct answer: