The length of the plank is l. The bullet experiences a constant resistive force F inside the block. The minimum value of \[{{v}_{0}}\] such that it is able to come out of the plank is
A) \[\sqrt{\frac{F/m}{{{M}^{2}}}}\]
B) \[\sqrt{\frac{2F\ell (M+m)}{Mm}}\]
C) \[\sqrt{\frac{2F\ell m}{{{M}^{2}}}}\]
D) \[\sqrt{\frac{F\ell (M+m)}{Mm}}\]
Correct Answer: B
Solution :
[b] From Newton's third law, a force F acts on the block in forward direction. Acceleration of block \[{{a}_{1}}=\frac{F}{M}\] 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, \[{{v}_{0}}=\sqrt{\frac{2F\ell (M+m)}{Mm}}\]
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