Question

A ball of mass $1\text{kg}$ is thrown with a velocity of $6\text{m/s}$ at a stone of unknown mass initially at rest. If the velocity of the stone after the elastic collision with the ball is $1.5\text{m/s}$, what is the mass of the stone?

• A. $8\text{kg}$
• B. $5\text{kg}$
• C. $7\text{kg}$
• D. $10\text{kg}$

Answer 1

The correct option is C $7\text{kg}$

Let the ball be body A and the stone be body B.
We have, $m_A=1\text{kg},m_B=x\text{kg}{u}_A=6\text{m/s},u_B=0\text{m/s}{v}_B=1.5\text{m/s}$

As we know,
$u_A-u_B=v_B-v_A$
$6-0=1.5-v_A$
$v_A=-4.5\text{m/s}$
Applying the law of conservation of momentum we get,
$m_A{u}_A+m_B{u}_B=m_A{v}_A+m_B{v}_B$
$\Rightarrow (1\times 6)+(x\times 0)=(1\times -4.5)+(x\times 1.5)$
$6+4.5=x\times 1.5$
$x=\frac{10.5}{1.5}=7\text{kg}$