A) \[\sqrt{\frac{F\ell /m}{{{M}^{2}}}}\]
B) \[\begin{align} & \sqrt{\frac{2F\ell \,(M+m)}{Mm}} \\ & \\ \end{align}\]
C) \[\begin{align} & \sqrt{\frac{2F\ell \,m}{{{M}^{2}}}} \\ & \\ \end{align}\]
D) \[\sqrt{\frac{F\ell \,(M+m)}{M{{m}^{{}}}}}\]
Correct Answer: B
Solution :
[b] From Newton's third law a force F acts on the block in forward direction. Acceleration of black \[{{a}_{1}}=\frac{F}{M}\] Retardation of bullet \[{{a}_{2}}=\frac{F}{m}\] Relative retardation of bullet \[{{a}_{r}}={{a}_{1}}+{{a}_{2}}=\frac{F(M+m)}{Mm}\] Applying \[{{v}^{2}}={{u}^{2}}-2{{a}_{r}}\ell \] \[0={{v}_{0}}^{2}-\frac{2F(M+m)}{Mm}.\ell \] Therefore, minimum value of \[{{V}_{0}}\]is Or \[{{V}_{0}}=\sqrt{\frac{2F\ell (M+m)}{Mm}}\]You need to login to perform this action.
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