Question

A bullet of mass $20\text{g}$ strikes a block of mass $180\text{g}$. The bullet remains embedded in the block. Find the amplitude of the resulting SHM (all surfaces are fricitonless]

• A. $2.36\text{cm}$
• B. $1.26\text{cm}$
• C. $4\text{cm}$
• D. $2.75\text{cm}$

Answer 1

The correct option is B $1.26\text{cm}$

Let $v$ be the combined velocity of system just after collision.
Using conservation of linear momentum
$m{v}_0+(M\times 0)=(m+M)v$
$v=\frac{m{v}_0}{m+M}=\frac{20\times 2}{200}=0.2\text{m/s}$
and this will be the maximum speed of mass attached to the string and this position will be mean position as extension of spring.
So $v=A\omega$
$\Rightarrow 0.2=\sqrt{\left(\frac{k}{m+M}\right)}A$
$\Rightarrow A=\frac{0.2}{\sqrt{\left(\frac{k}{m+M}\right)}}$
$\Rightarrow A=\frac{0.2}{\sqrt{\frac{50}{0.2}}}=0.0126\text{m}$
$\Rightarrow A=1.26\text{cm}$