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

Options

A. `A(sqrt((k)/(M)))`
B. `(A(sqrt(3)))/(2) (sqrt((k)/(M)))`
C. `A(sqrt(3)) (sqrt((k)/(M)))`
D. `2a (sqrt((M)/(k)))`

Answer

C

Explanation

`v_(0)=V_(I)=(omega)A = (sqrt((k)/(M)))A`
`v_r=sqrt((v_(0))^(2) +(v_(1))^(2) -2(V_(0)) cos 120^(@))`
`sqrt(3) A (sqrt((k)/(M)))`.