Question

A spring scale is adjusted to read zero. Particles of mass 1 g fall on the pan of the scale and collide elastically and they rebound upward with the same speed. If the height of fall of panicles is 2 m and their rate of collision is 100 particles per second, then the scale reading in grams will be $(g=9.8m/{{s}^{2}})$

• A. 1000 g
• B. 1100g
• C. 1200 g
• D. 1252 g

Answer 1

Answer: (D)

1252 g

Answer 2

The velocity attained by particle on falling from height $2m$ . $v=\sqrt{2gh}=\sqrt{2\times g\times 2}=2\sqrt{g}$ Rate of change of momentum of 100 particles $=2mv\times 100=200\text{ }mv$ From Newton's law, rate of change of momentum is equal to force. Force $=200\text{ }mv$ $=200\times 1\times {{10}^{-3}}\times 2\sqrt{g}$ $=1252g$ (reading).