A system of two blocks of masses m = 2 kg and M = 8 kg is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is 0.5. The maximum horizontal force F that can be applied to the block of mass M so that the blocks move together will be :

Solution

Physics sir · 4 steps

Only friction pulls the top block, so friction sets the largest acceleration the pair can share.

1. Who drives m. F acts on M only. The block m moves because static friction from M pulls it forward, and the table is smooth, so there is no other horizontal force on the pair.
2. Limit on m. Static friction can be at most μ m g. So the largest acceleration m can have is aₘₐₓ = (μ m g)/m = μ g = 0.5 × 9.8 = 4.9 m s⁻².
3. Whole system. Moving together, both blocks share this acceleration. Friction between them is internal, so for the pair F = (m + M) a.

   Fₘₐₓ = (m+M) μ g = (2+8) × 4.9 = 49 N

4. So. The largest force for which the blocks move together is 49 N, option (c).

The idea to keep. Find the block that is pushed only by friction. Its maximum acceleration is μ g. Then multiply by the total mass to get the largest force on the system.

Answer from the NTA final answer key. Solution by PrepWiser.