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(A) Let the system accelerate with acceleration $a$ such that $M_1$ moves down the incline $\alpha$ and $M_2$ moves up the incline $\beta$.For mass $M

Vedclass · Accepted Answer

$\frac{M_1 M_2(\sin \alpha+\sin \beta) g}{M_1+M_2}$

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(A) Let the system accelerate with acceleration $a$ such that $M_1$ moves down the incline $\alpha$ and $M_2$ moves up the incline $\beta$.For mass $M_1$: $M_1 g \sin \alpha - T = M_1 a$  (Equation $1$)For mass $M_2$: $T - M_2 g \sin \beta = M_2 a$  (Equation $2$)Adding Equation $1$ and Equation $2$:$(M_1 g \sin \alpha - T) + (T - M_2 g \sin \beta) = (M_1 + M_2) a$$g(M_1 \sin \alpha - M_2 \sin \beta) = (M_1 + M_2) a$$a = \frac{g(M_1 \sin \alpha - M_2 \sin \beta)}{M_1 + M_2}$Substituting $a$ into Equation $2$:$T = M_2 a + M_2 g \sin \beta = M_2 \left[ \frac{g(M_1 \sin \alpha - M_2 \sin \beta)}{M_1 + M_2} + g \sin \beta \right]$$T = M_2 g \left[ \frac{M_1 \sin \alpha - M_2 \sin \beta + M_1 \sin \beta + M_2 \sin \beta}{M_1 + M_2} \right]$$T = \frac{M_1 M_2 g(\sin \alpha + \sin \beta)}{M_1 + M_2}$

Two masses $M_1$ and $M_2$ are attached to the ends of a light string which passes over a massless pulley attached to the top of a double inclined smooth plane of angles of inclination $\alpha$ and $\beta$. The tension in the string is:

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