Question

The block A in figure shown moves at speed v towards B placed in equilibrium. All collisions to take place are elastic and surfaces are frictionless. Find the time period of the periodic motions of the two blocks.

• A. $\frac{2L}{v}+\pi \sqrt{\frac{2m}{k}}$
• B. $\frac{L}{v}+\pi \sqrt{\frac{2m}{k}}$
• C. $\frac{L}{v}+\pi \sqrt{\frac{m}{k}}$
• D. $\frac{2L}{v}+\pi \sqrt{\frac{m}{k}}$

Answer 1

The correct option is D $\frac{2L}{v}+\pi \sqrt{\frac{m}{k}}$

for block B $T=2\pi \sqrt{\frac{m}{k}}$
for block A $T=\frac{2L}{v}+\frac{2\pi \sqrt{\frac{m}{k}}}{2}$
or $T=\frac{2L}{v}+\pi \sqrt{\frac{m}{k}}$