Question

If a small block of mass m is placed gently on M when it is passing through its mean position. Find it's new amplitude of SHM, if initial amplitude is A.

a}\(\sqrt { M\over M+m}\)(A)

b}\(\sqrt{ M+m\over M}\)(A)

C}\(\sqrt{ M+m\over 2 M}\) (A)

d}\(\sqrt{ M\over M-m}(A)\)

Answer 1

Velocity at mean positon is A\(\omega\) 

Conserving Momentum MA\(\omega_0 +(M+m)V'\)

\(V'={MA\omega_o \over M+m} =(A')\sqrt{K\over M+m}\)

\(A'={ MA\sqrt{K\over M}\over M+m} \times{ \sqrt{M+m\over K}}=\sqrt{ M\over (M+m)}A\)

 

Hence , B option is correct