Question

An explosion blows a rock in to three pieces . Two pieces go off at right angles to each other . One of these two pieces of mass 1kg moves with 12 m/s and other of mass 2 kg moves with 8 m/s . If he velocity of the third piece is 40 m/s then its mass is :

• A. 0.5 kg
• B. 5 kg
• C. 0.25 kg
• D. 0.75 kg

Answer 1

The correct option is A 0.5 kg

Rock was initially at rest so the net linear momentum of the three masses should be zero after the explosion.

Now momentum of the first mass is $p_1=1kg\times 12m/s=12kgm/s$

Now momentum of the second mass is $p_2=2kg\times 8m/s=16kgm/s$

Since momentum is a $vector$ quantity and the $p_1$ and $p_2$ are at ${90}^0$ so their resultant will be $\sqrt[2]{2p_1^2+p_2^2}=\sqrt[2]{2144+256}=20kgm/s$

If mass of the third mass is $m$ then its momentum will be $m\times 40=40m$

And off course this should be opposite and equal to the net of $p_1$ and $p_2$ to make the net as $zero$ i.e equal to initial

value.

So $40m=20$ so $m=0.5Kg$

Option A is correct.