First slide

Second law

Question

An object flying in air with velocity
$\large (20\hat i + 25\hat j - 12\hat k)$
suddenly breaks in two pieces whose masses are in the ratio 1 : 5. The smaller mass flies off with a velocity
$\large (100\hat i + 35\hat j + 8\hat k)$
. The velocity of the larger piece will be :

Moderate

A

$4\hat i + 23\hat j - 16\hat k$
B

$\large - 100\hat i - 35\hat j - 8\hat k$
C

$\large 20\hat i + 15\hat j - 80\hat k$
D

$\fn_phv \large - 20\hat i - 15\hat j - 80\hat k$

Solution

By conservation of linear momentum
$\large {\vec P_i} = {\vec P_f}$
$\large m{\vec v_i} = \left( {\frac{m}{6}{{\vec v}_1} + \frac{{5m}}{6}{{\vec v}_2}} \right)$
$\large {\vec v_i} = \left( {\frac{{{{\vec v}_1}}}{6} + \frac{5}{6}{{\vec v}_2}} \right)$
$\large 20\hat i + 25\hat j - 12\hat k = \frac{{\left( {100\hat i + 35\hat j + 8\hat k} \right)}}{6} + \frac{{5{{\vec v}_2}}}{6}$
$\large 120\hat i + 150\hat j - 72\hat k = 100\hat i + 35\hat j + 8\hat k + 5{\vec v_2}$
$20\hat i + 115\hat j - 80\hat k = 5{\vec v_2}$
$\large {\vec v_2} = \frac{{20\hat i + 115\hat j - 80\hat k}}{5}$
$\large 4\hat i + 23\hat j - 16\hat k$

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