Question

A grenade having mass of 10 kg flying horizontally with a velocity of 10 m/s explodes into two fragments. The larger fragment has a velocity 25 m/s in the direction of the initial velocity of the grenade. The smaller fragment has a velocity of 12.5 m/s in the opposite direction. The masses of the fragments are

• A. 2 kg, 8 kg
• B. 3 kg, 7 kg
• C. 4 kg, 6 kg
• D. 4.5 kg, 5.5 kg

Answer 1

The correct option is C 4 kg, 6 kg

Let the mass of the larger fragment be m kg.
Then, the mass of the smaller fragment = (10 – m) kg
According to the law of conservation of linear momentum,
Initial linear momentum = Final linear momentum
$\Rightarrow 10\times 10=m\times 25–(10–m)\times 12.5$
$\Rightarrow 100=25m–125+12.5m$
$\Rightarrow 225=37.5m$
$\Rightarrow m=\frac{225}{37.5}$
$=6kg$
$\therefore$ Mass of the heavier fragment = 6 kg
Mass of the smaller fragment = 10 – 6 = 4 kg