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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 ms–1 and 2 kg second part moving with a velocity of 8 ms–1. If the third part flies off with a velocity of 4 ms–1, its mass would be :
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- 7 kg
- 17 kg
- 3 kg
- 5 kg
Correct Option: D
Let two parts of the rock move along x-axis and y-axis respectively.
If M and v be the mass and velocities of third part then
Mv cos θ = 12
Mv sin θ =16
| tan θ = | = | |||
| 12 | 3 |
| cos θ = | ||
| 5 |
v = 4 m /s
| M = | ||
| v cos θ |
| M = | = | = 5 kg | ||
| 4 × 3 | 12 |
