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Consider the given arrangement of infinite uniform discs$A_1,A_2,A_3,...,A_n$, each of mass m and radius R. Each disc is kept on a stair. Height of each stair is R. Strings are wrapped around discs whose another end is attached to center of discs as shown. All surfaces are sufficiently rough, so that there is no slipping anywhere. A tangential horizontal force equal to mg is applied on disc $A_1$. Whole arrangement is shown in the figure. Answer the following two questions

(1) Choose the correct option(s)
(A) Acceleration of com of $A_1$ is g
(B) Acceleration of com of $A_6$ is $\frac{g}{32}$
(C) Angular acceleration of $A_7$ is $\frac{g}{64R}$
(D) Angular acceleration of $A_5$ is $\frac{g}{16R}$

(2) Choose the correct option(s)
(A) Tension in the string connecting $A_1$ and $A_2$ is $\frac{mg}{2}$
(B) Tension in the string connecting $A_5$ and $A_6$ is $\frac{mg}{32}$
(C) Frictional force between $A_8$ and stair is $\frac{mg}{256}$
(D) Frictional force between $A_3$ and stair is $\frac{mg}{8}$

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  • $\begingroup$ Could anyone tell why friction at each disc and tension are equal and opposite? I have written $2$ equation- equation of motion and torque equation, but there are $3$ variables- $a,\ f,\ T$. As for the question, it is obvious that all must be true if anyone of them is true. $\endgroup$
    – Sameer Baheti
    Jul 9, 2020 at 19:24

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