Two wooden blocks of masses M and m are place | vedclass

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Question

(A) Let the acceleration of the system be $a$. Since the block $m$ is stationary with respect to the block $M$,both move with the same acceleration $a

Vedclass · Accepted Answer

$(M+m) g 	an \beta$

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(A) Let the acceleration of the system be $a$. Since the block $m$ is stationary with respect to the block $M$,both move with the same acceleration $a$.For the block $m$,the forces acting in the frame of the block $M$ (pseudo force frame) are:$1$. Pseudo force $ma$ acting horizontally to the left.$2$. Gravitational force $mg$ acting vertically downwards.$3$. Normal force $N$ perpendicular to the inclined surface.For $m$ to remain stationary on the incline,the component of pseudo force along the incline must balance the component of gravitational force along the incline:$ma \cos \beta = mg \sin \beta$$a = g \frac{\sin \beta}{\cos \beta} = g 	an \beta$Now,considering the whole system of mass $(M+m)$ moving with acceleration $a$ under the force $P$:$P = (M+m) a$Substituting the value of $a$:$P = (M+m) g 	an \beta$

Two wooden blocks of masses $M$ and $m$ are placed on a smooth horizontal surface as shown in the figure. If a force $P$ is applied to the system as shown in the figure such that the mass $m$ remains stationary with respect to the block of mass $M$,then the magnitude of the force $P$ is

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