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An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 $ms^{-1}$ and the second part of mass 2 kg moves with 8 $ms^{-1}$ speed. If the third part flies off with 4 $ms^{-1}$ speed, then its mass is:
A
17 kg
B
3 kg
C
5 kg
D
7 kg
Detailed Solution
By conservation of momentum, the third part balances the resultant of the first two:
$m(4) = \sqrt{(1\times12)^2 + (2\times8)^2} = 20$
$m = 5$ kg