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.

• A. 62.5 N
• B. 150 N
• C. 31.25 N
• D. 50 N

Answer 1

The correct option is C

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.

$N_2=N_1=F,f_{t_1}=\mu N_1=0.4F,f_{t_2}=\mu N_2=0.4F$

For 15 kg : $T+f_{t_1}=15g\Rightarrow T+0.4F=15g$ ......................(i)

For 25 kg : $2T=f_{t_1}+f_{t_2}+25g$

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

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