First slide

Plane mirror

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

Moderate

A

$A \sqrt{\frac{K}{M}}$
B

$\frac{A}{\sqrt{2}} \sqrt{\frac{K}{M}}$
C

$A \sqrt{2} \sqrt{\frac{K}{M}}$
D

$A \sqrt{\frac{M}{K}}$

Solution

$\begin{array}{l} v_{o} = ω A (- \hat{j}) \\ v_{I} = ω A (- \hat{i}) \\ V e l o c i t y o f o b j e c t w r t i m a g e : \\ v_{O I} = v_{o} - v_{i} = ω A \hat{i} - ω A \hat{j} \\ υ_{\max} = υ \sqrt{2} = \sqrt{2} ω A = \sqrt{2} A \sqrt{\frac{K}{M}} \end{array}$

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