Question

A shell of mass 100 kg is fired horizontally from a cannon having a mass of $5\times {10}^3$ kg. The kinetic energy of the shell at the end of the barrel is $7.5\times {10}^{6}J$. Then the kinetic energy imparted by the velocity of recoil is

• A. $2\times {10}^{5}J$
• B. $7.5\times {10}^{6}J$
• C. $14.9\times {10}^{6}J$
• D. ${10}^{5}J$

Answer 1

Answer: (C)

$14.9\times {10}^{6}J$

$E_1=0.5\times m_1{v_1}^2$

$⟹7.5\times {10}^6=0.5\times 100\times {v_1}^2$

$v_1=3.87\times {10}^{2}m/s$

Using conservation of momentum,

$m_1{v}_1=m_2{v}_2$

$100\times 3.87\times {10}^2=5\times {10}^3\times v_2$

$v_2=7.74m/s$

Hence, the kinetic energy imparted by the velocity of recoil $E_2=0.5\times 5\times {10}^3\times {7.74}^2$

$E_2=14.9\times {10}^{6}J$