A system consists of three masses \[{{m}_{1}},{{m}_{2}}\] and \[{{m}_{3}}\] connected by a string passing over a pulley P. The mass \[{{m}_{1}}\] hangs freely and \[{{m}_{2}}\] and \[{{m}_{3}}\] are on a rough horizontal table (the coefficient of friction \[=\mu \]). The pulley is frictionless and of [NEET 2014] |
negligible mass. The downward acceleration of mass \[{{m}_{1}}\] is (Assume,\[{{m}_{1}}={{m}_{2}}={{m}_{3}}=m\]) |
A) \[\frac{g(1-g\mu )}{9}\]
B) \[\frac{2g\mu }{3}\]
C) \[\frac{g(1-2\mu )}{3}\]
D) \[\frac{g(1-2\mu )}{2}\]
Correct Answer: C
Solution :
First of all consider the forces on the blocks |
For the 1st block, \[[\because \,{{m}_{1}}={{m}_{2}}={{m}_{3}}]\] |
\[mg-B=m\times a\] (ii) |
\[\Rightarrow \] Let us consider 2nd and 3rd block as a system |
So, \[{{T}_{1}}-2\mu mg\,=2m\times a\] (i) |
Solving Eqs. (i) and (ii), |
\[\Rightarrow \] \[mg-{{T}_{1}}=m\times a\] |
\[{{T}_{1}}-2\mu mg=2m\times a\] |
\[mg(1-2\mu )=3m\times a\] |
\[a=\frac{2}{3}(1-2\mu )\] |
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