Question

A block of mass $100g$ attached to a spring of stiffness $100N/m$ is lying on a frictionless floor as shown. The block is moved to compress the spring by $10cm$ and released. If the collision with the wall is elastic the time period of motion is:

• A. $0.2s$
• B. $0.166s$
• C. $0.155s$
• D. $0.133s$

Answer 1

Answer: (D)

$0.133s$

5 cm is $\frac{A}{2}$ and $O$ to $\frac{A}{2}$, the time taken is $\frac{T}{12}$.

$T=t_{LHS}+t_{RHS}=\frac{T}{2}+2\left(\frac{T}{12}\right)$
$=\frac{2}{3}T=\frac{2}{3}\left(2\pi \right)\sqrt{\frac{m}{k}}$
$=\frac{4\pi }{3}\sqrt{\frac{0.1}{100}}$ $=0.133$ s