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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Center of Mass, Momentum and Collision

NTA Abhyas 2020 · Physics · Center of Mass, Momentum and Collision

Two particles of masses 2 kg and 3 kg are projected horizontally in...

Two particles of masses 22 kg and 33 kg are projected horizontally in opposite directions from the top of a tower of height 39.2m39. 2m with velocities 5ms−15ms^{- 1} and 10ms−110ms^{- 1} respectively. The horizontal range of the centre of mass of two particles is [g = 9. 8ms^{- 2}]]

Options

  1. A828\sqrt{2} m in the direction of 2 kg
  2. B828\sqrt{2} m in the direction of 3 kg
  3. C8\sqrt{8} m in the direction of 2 kg
  4. D8\sqrt{8} m in the direction of 3 kg

Correct answer

B. 828\sqrt{2} m in the direction of 3 kg

Step-by-step solution

Range of C.M =Vcm2hg= {V}_{cm}\sqrt{\dfrac{2h}{g}}

Vcm=m1v1+m2v2m1+m2{V}_{cm} = \dfrac{{m}_{1}{v}_{1} + {m}_{2}{v}_{2}}{{m}_{1} + {m}_{2}}

Vcom=−2×5+3×102+3=4m/s{V}_{com} = \dfrac{- 2 \times 5 + 3 \times 10}{2 + 3} = 4m / s

Range =42×39.29.8=82= 4\sqrt{\dfrac{2 \times 39.2}{9.8}} = 8\sqrt{2}
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