Two blocks $$A(2$$ $$kg)$$ and $$B(5$$ $$kg)$$ rest one over the other on a smooth horizontal plane. The coefficient of static and dynamic friction between A and B is the same and is equal to $$0.60$$. The maximum horizontal force that can be applied to B in order that both A and B do not have relative motion is TAKE $$g=$$ $$10$$ $$ms-2$$

Question

Two blocks $$A(2$$ $$kg)$$ and $$B(5$$ $$kg)$$ rest one over the other on a smooth horizontal plane. The coefficient of static and dynamic friction between A and B is the same and is equal to $$0.60$$. The maximum horizontal force that can be applied to B in order that both A and B do not have relative motion is   TAKE $$g=$$ $$10$$ $$ms-2$$

Infinity Learn · Accepted Answer

Let due to a force F on B, both blocks A and B, both blocks A and B move together. In this case,$$F=mA+mBa=(2+5)a$$∴ $$a=(F/7)Now$$ force on $$A=m$$ $$a=2$$×(F/7)For$$ no relative motion between A and B, $$(2F$$ $$/$$ $$7) must not exceed the limiting force of friction between, A and B. The limiting force of friction between A and B is given byμ$$mAg=0$$⋅$$6$$×$$2$$×g∴ $$2F7=0$$⋅$$6$$×$$2$$×$$gF=4$$⋅$$2N$$ $$g=4$$⋅$$2kgf$$.

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