Question

A body of mass 1 kg initially at rest explodes and breaks into three fragments of masses in the ratio 1:1:3. The two pieces of equal mass fly off perpendicular to each other with a speed of 15 ms${}^{-1}$ each. The speed of the heavier fragment is :

• A. 45 ms${}^{-1}$
• B. 15 ms${}^{-1}$
• C. 5 ms${}^{-1}$
• D. 5$\sqrt{2}$ ms${}^{-1}$

Answer 1

The correct option is D 5$\sqrt{2}$ ms${}^{-1}$

Since 1Kg mass is divided in ratio $1:1:3$ the masses are
$m_1=m_2=\frac{1}{5}$ and $m_3=\frac{3}{5}$
Now, the two pieces of equal mass fly off perpendicular to other hence,
$(m_1{v}_1{)}^2+(m_2{v}_2{)}^2=(m_3{v}_3{)}^2$
${\left(\frac{3}{5}{v}_3\right)}^2=(\frac{1}{5}15{)}^2+(\frac{1}{5}15{)}^2$
${\left(\frac{3}{5}{v}_3\right)}^2=(3{)}^2+(3{)}^2$
${\left(\frac{3}{5}{v}_3\right)}^2=18$
$\frac{3}{5}{v}_3=\sqrt{18}$
$v_3=\sqrt{1}8\times \frac{5}{3}$
$v_3=3\sqrt{2}\times \frac{5}{3}=5\sqrt{2}m{s}^{-1}$