A block of mass $$M1$$ $$=$$ $$10$$ kg is placed on a slab of mass $$M2$$ $$=30kg$$, The slab lies on a frictionless horizontal surface as shown in fig. The coefficient of staticfriction between the block and slab is µ$$1$$ $$=0.5$$ and that of dynamic friction is µ$$2$$ $$=0.15$$.A force F $$=40N$$ acts on block $$M1$$. What will be the acceleration with which the slab will move? (Take$$ $$g=10m/s2$$ $$)

Question

A block of mass $$M1$$ $$=$$ $$10$$ kg is placed on a slab of mass $$M2$$ $$=30kg$$, The slab lies on a frictionless horizontal surface as shown in fig. The coefficient of staticfriction between the block and slab is µ$$1$$ $$=0.5$$ and that of dynamic friction is µ$$2$$ $$=0.15$$.A force F $$=40N$$ acts on block $$M1$$. What will be the acceleration with which the slab will move?  (Take$$ $$g=10m/s2$$ $$)

Infinity Learn · Accepted Answer

The slab will move due to the force exerted on it due to the friction between the block and slab. When the force acting on the block is less than the static friction, it will not move. The total force causing acceleration of $$M1$$ and $$M2$$ both will be the force applied.Limiting friction $$=$$μ$$M1g=0$$⋅$$5$$×$$10$$×$$10=50NSo$$, the applied force will not cause motion of $$M1$$.∴The acceleration of system $$a=40N(10+30)kg=1m/s2$$

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