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Question

If the coefficient of friction between all surfaces (fig.) is 0.4, then find the minimum force F to have equilibrium of the system.


  1. 50 N

  2. 62.5 N

  3. 150 N

  4. 31.25 N


Solution

The correct option is D

31.25 N


in the absence of fiction, we can find that 15kg will accelerate downwards and 25kg upwards. So various forces acting on these will be as shown.

N2=N1=F,ft1=μN1=0.4F,ft2=μN2=0.4F

For 15 kg : T+ft1=15gT+0.4F=15g   ......................(i)

For 25 kg : 2T=ft1+ft2+25g

2T=0.8F+25g      ........................(ii)

Solve Eqs. (i) and (ii) to get F = 31.25 N

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