# If a small block of mass m is placed gently on M when it is passing through its mean position.

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

verified

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