363463
Assertion : A bullet is fired from a rifle. If the rifle recoils freely, the kinetic energy of rifle is less than that of the bullet. Reason : In the case of rifle - bullet system the law of conservation of momentum violates.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
There is no external force on the system (Rifle + Bullet) [Denote 'Rifle' by subscript \(R\)., and 'Bullet' by subscript \(B\).] \(\Rightarrow\) Conservation of linear momentum holds good \(\Rightarrow\) 'Reason' statement is not correct. Let \(m\) and \(v\) represent mass and find velocity. (Their masses do not differ much.) Initially, system was at rest \(\Rightarrow 0=m_{B} v_{B}+m_{R} v_{R}\) \(\Rightarrow v_{R}=-\left(\dfrac{m_{B}}{m_{R}}\right) v_{B}\) Where negative sign is due to 'recoil'. \({m_R} > {m_B}\) \( \Rightarrow \left| {{v_R}} \right| < \left| {{v_B}} \right|\) \( \Rightarrow \frac{1}{2}{m_R}v_R^2 < \frac{1}{2}{m_B}v_B^2\) \( \Rightarrow {\rm{Assertion}}\,\,{\rm{is}}\,\,{\rm{correct}}\) So correct option is (3).
