Looking for classes? Ksquare Career Institute, Bengaluru →
An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are, 1 kg first part moving with a velocity of 12 m $s^{-1}$ and 2 kg second part moving with a velocity of 8 m $s^{-1}$. If the third part flies off with a velocity of 4 m $s^{-1}$, its mass would be
A
3 kg
B
5 kg
C
7 kg
D
17 kg
Detailed Solution
The rock is initially at rest, so the total momentum after the explosion must be zero.
Momentum of the first part: $p_1 = 1\times12 = 12$ kg m/s
Momentum of the second part: $p_2 = 2\times8 = 16$ kg m/s
These are at right angles, so their resultant is $\sqrt{12^2 + 16^2} = \sqrt{400} = 20$ kg m/s
The third part must have an equal and opposite momentum: $m_3\times4 = 20$
$m_3 = 5$ kg
Momentum of the first part: $p_1 = 1\times12 = 12$ kg m/s
Momentum of the second part: $p_2 = 2\times8 = 16$ kg m/s
These are at right angles, so their resultant is $\sqrt{12^2 + 16^2} = \sqrt{400} = 20$ kg m/s
The third part must have an equal and opposite momentum: $m_3\times4 = 20$
$m_3 = 5$ kg