Question

Six identical uniform rods PQ, QR, RS, ST, TU and UP each weighing W are freely joined at their ends to form a hexagon. The rod PQ is fixed in a horizontal position and middle points of PQ and ST are connected by a vertical string. The tension in string is

• A. W
• B. 3W
• C. 2W
• D. 4W

Answer 1

Answer: (B)

3W

Answer 2

Let a small displacement be given to the system in vertical plane in frame such that ST remains horizontal then let vertical displacement of centres of rods UP and QR be y then vertical displacement of centres of UT and RS will be 3y and that of TS will by 4y. Equating the total virtual work to zero we get

(W + W)δy + (W + W)3δy + W(4δy) – T(4δy) = 0

(where T is the lension in thread)

or 2W + 6 W + 4W = 4T

or T = 3W