A shell of mass 200 ~g is ejected from a gun of mass 4 ~kg by an explosion that generates 1.05 ~kJ of energy. The initial velocity of the shell is

Correct answer: A. 100 ~ms^ -1 Key Idea: In the given problem conservation of linear momentum and energy hold good. Conservation of momentum yields. aligned & m_1 v_1+m_2 y_2=0 & or 4 y_1+0.2 y_2=0 aligned Conservation of energy yields array l &(1)/(2) m_1 y_1^2+(1)/(2) m_2 y_2^2=1050 & or (1)/(2) × 4 y_1^2+(1)/(2) × 0.2 × y_2^2=1050 & or 2 v_1^2+0.1 v_2^2=1050 array Solving Eqs. (i) and (ii), we have v_1=100 ~m / s

NEET 2008

Exam: NEET
Year: 2008
Subject: Physics
Chapter: Center of Mass, Momentum and Collision

NEET 2008 · Physics · Center of Mass, Momentum and Collision

A shell of mass 200 ~g is ejected from a gun of mass 4 ~kg by an...

A shell of mass

200 \mathrm{~g}

is ejected from a gun of mass

4 \mathrm{~kg}

by an explosion that generates

1.05 \mathrm{~kJ}

of energy. The initial velocity of the shell is

Options

A $100 \mathrm{~ms}^{-1}$
B $80 \mathrm{~ms}^{-1}$
C $40 \mathrm{~ms}^{-1}$
D $120 \mathrm{~ms}^{-1}$

Correct answer

A. $100 \mathrm{~ms}^{-1}$

Step-by-step solution

Key Idea: In the given problem conservation of linear momentum and energy hold good. Conservation of momentum yields.

\begin{aligned} & m_1 v_1+m_2 y_2=0 \\ & \text{or } 4 y_1+0.2 y_2=0 \end{aligned}

Conservation

of energy yields

\begin{array}{l} &\frac{1}{2} m_1 y_1^2+\frac{1}{2} m_2 y_2^2=1050 \\ & \text{or } \frac{1}{2} \times 4 y_1^2+\frac{1}{2} \times 0.2 \times y_2^2=1050 \\ & \text{or } 2 v_1^2+0.1 v_2^2=1050 \end{array}

Solving Eqs. (i) and (ii), we have

v_1=100 \mathrm{~m} / \mathrm{s}$

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