(i) Four small blocks are interconnected with light strings and placed over a fixed sphere as shown. Blocks A, B and C are identical each having mass m = 1 kg. Block D has a mass of m´ = 2 kg. The coefficient of friction between the blocks and the sphere is `mu = 0.5`. The system is released from the position shown in figure.

(a) Find the tension in each string. Which string has largest tension?
(b) Find the friction force acting on each block.
[Take `"tan"37^(@) = (3)/(4) , g = 10 m//s^(2)`]
(ii) A fixed square prism ABCD has its axis horizontal and perpendicular to the plane of the figure. The face AB makes `45^(@)` with the vertical. On the upper faces AB and BC of the prism there are light bodies P and Q respectively. The two bodies (P and Q) are connected using a string `S_(1)` and strings `S_(0)` and `S_(2)` are hanging from P and Q respectively. All strings are mass less, and inextensible. String` S_(1)` is horizontal and the other two strings are vertical. The coefficient of friction between the bodies and the prism is `mu_(0)` . Assume that P and Q always remain in contact with the prism.
(a) If tension in `S_(0)` is `T_(0)`, find the minimum tension `(T_(1))` in `S_(1)` to keep the body P at rest.
(b) A mass `M_(0)` is tied to the lower end of string `S_(0)` and another mass `m_(2)` is tied to `S_(2)` . Find the minimum value of m2 so as to keep P and Q at rest.

Answer

(a) `T_(BC) = 10N ; T_(AB) = 12N ; T_(AD) = 7N`
(b) `f_(C) = 0 ; f_(B) = 4N ; f_(A) = 5N ; f_(D) = 5N`
(ii) (a) `T_(1) = ((1- mu_(0))/(1 + mu_(0))) T_(0)`
(b) `m_(2) = ((1 - mu_(0))/(1 + mu_(0)))^(2) M_(0)`