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A small particle of mass m moving inside...

A small particle of mass m moving inside a heavy, hollow and straight tube along the tube axis undergoes elastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other end is fitted with a heavy movable flat piston as shown in figure. When the distance of the piston from closed end is `L = L_0` the particle speed is `v = v_0` The piston is moved inward at a very low speed V such that `V < < (dL)/(L) v_0`, where dL is the infinitesimal displacement of the piston. Which of the following statements(s) is(are) correct?

A

The rate at which the particle strikes the piston is v/L

B

After each collision with the piston , the particle speed increases by 2V .

C

The particles kinetic energy increases by a factor of 4 when the piston is moved inward from `vec(L)_(0) " to" 1/2 L_(0)`

D

If the piston moves inward by dL , the particle speed increases by `2 (dL)/L `.

Text Solution

Verified by Experts

The correct Answer is:
B, C
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