Question

Two balls $A$ and $B$ of masses $2\text{kg}$ each are moving with speeds $1\text{m/s}$ and $2\text{m/s}$ on a frictionless surface. After colliding, ball $A$ returns back with speed $0.5\text{m/s}$, then the maximum potential energy of deformation is

• A. $45\text{J}$
• B. $24\text{J}$
• C. $4.5\text{J}$
• D. $2.4\text{J}$

Answer 1

The correct option is C $4.5\text{J}$

Given, $m_A=2\text{kg};m_B=2\text{kg}$
$u_A=1\text{m/s},u_B=-2\text{m/s}$
$v_A=-0.5\text{m/s}$
Applying PCLM,
$m_A{u}_A+m_B{v}_B=m_A{v}_A+m_B{v}_B$
$2\left(1\right)+2(-2)=2(-0.5)+2\left(v_B\right)$
$\Rightarrow v_B=-0.5\text{m/s}$

Common velocity of balls during collision, $v=\frac{m_1{u}_1+m_2{u}_2}{m_1+m_2}$
$=\frac{2\left(1\right)+2(-2)}{4}$
$=-\frac{1}{2}\text{m/s}$

Max, potential energy of deformation = Initial K.E - K.E during maximum compression
$U_{max}=\frac{1}{2}\left[2\right(1{)}^2+2(-2{)}^2]-\frac{1}{2}\left[\right(2+2\left){\left(\frac{-1}{2}\right)}^2\right]$
$\Rightarrow U_{max}=4.5\text{J}$