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 stationary

B) For one unique value of F, blocks will be stationary

C) Blocks cannot be stationary for any value of F because all surfaces are smooth

D) Both (1) and (2)

Correct Answer: D

Solution :

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).