Question

An insect of negligible mass is sitting on a block of mass M, tied with a spring of force constant k. The block performs simple harmonic motion with amplitude A in front of a plane mirror placed as shown. The maximum speed of insect relative to its image will be

• A. $A\sqrt{\frac{k}{M}}$
• B. $\frac{A\sqrt{3}}{2}\sqrt{\frac{k}{M}}$
  
• C. $A\sqrt{3}\sqrt{\frac{k}{M}}$
  
• D. $2A\sqrt{\frac{M}{k}}$

Answer 1

The correct option is C $A\sqrt{3}\sqrt{\frac{k}{M}}$


Maximum speed of insect relative to its image

$\overrightarrow{V_{\frac{insect}{image}}}=\overrightarrow{V_{insect}}-\overrightarrow{V_{image}}$

$=V_{max}sin60-(-V_{max}sin60)$

$=2V_{max}\perp =2V_{max}sin{60}^{\circ }$

$=A\sqrt{3}\sqrt{\frac{k}{m}}$

$V_{max}=\omega A$


We know, $\Rightarrow V_{max}=\sqrt{\frac{k}{m}}A$

$\because {\omega }^2=\frac{k}{m}$ for SHM