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प्रश्न
The following figure shows two blocks of mass m and M connected by a string passing over a pulley. The horizontal table over which the mass m slides is smooth. The pulley has a radius r and moment of inertia I about its axis and it can freely rotate about this axis. Find the acceleration of the mass M assuming that the string does not slip on the pulley.
उत्तर
According to the equation, we have
\[Mg - T_1 = Ma ..........(1)\]
\[T_2 = ma ............(2)\]
\[ \Rightarrow \left( T_1 - T_2 \right) = \frac{Ia}{r^2}............(3)\left[\text{Because, }a = ra \right]\]
If we add the equations (1) and (2), we get
\[Mg + T_2 - T_1 = Ma + ma...........(4)\]
\[ \Rightarrow Mg - I\frac{a}{r^2} = Ma + ma\]
\[ \Rightarrow \left( M + m + \frac{I}{r^2} \right) a = Mg\]
\[ \Rightarrow a = \frac{Mg}{M + m + \frac{I}{r^2}}\]
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