Question

# A small block of mass 1 kg is placed over a plank of mass 2 kg. The length of the plank is 2 m. Coefficient of friction between the block and the plank is 0.5 and the ground over which plank is placed is smooth. A constant force F=30 N is applied on the plank in horizontal direction. The time after which the block will separate from the plank is (g=10 m/s2) approximately 0.73 s1.2 s0.62 s1.6 s

Solution

## The correct option is A 0.73 sMaximum frictional force between the block and the plank is fmax=μmg=(0.5)(1)(10)=5 N The free body diagrams of the block and the plank are shown here Acceleration of block a1=51=5 m/s2 Acceleration of plank a2=30−52=252 m/s2 ∴ Relative acceleration of plank a=a2−a1 or a=252−5=7.5 m/s2 ∴t=√2sa=√2×27.5=0.73 s

Suggest corrections