• # question_answer Two blocks of mass M and m are kept on the trolley whose all surfaces are smooth. Select the correct statement A) If F = 0 blocks cannot remain stationaryB) For one unique value of F, blocks will be stationaryC) Blocks cannot be stationary for any value of F because all surfaces are smoothD) Both (1) and (2)

Let us assume that the blocks do not move with respect to the trolley if the acceleration of the trolley is A. Making observations with respect to ground: $F=(M+m+{{m}_{o}})A\Rightarrow A=\frac{F}{(M+m+{{m}_{o}})}$ Making observations with respect to the trolley: $T=MA,T=mg$ $\Rightarrow$$MA=mg\Rightarrow \frac{MF}{(M+m+{{m}_{o}})}=mg$ $\therefore$    $F=\frac{(M+m+{{m}_{o}})mg}{M}$ Thus for $F=\frac{(M+m+{{m}_{o}})mg}{M}$the blocks remain at rest with respect to the trolley. From above relations for F = 0, A = 0 and T = 0, so the blocks move with respect to the trolley if F=0. Hence, the correction option is (d).