EXAMPLES XXI 375 



nected by a wire of resistance R ohms and inductance L henries. 

 If v is the voltage at any subsequent time t seconds then 



If R - 100 ohms, k - 5 x 10~ 7 farad and L = 10- 3 henry. 

 Express v in terms of t, having given that v = 500, -r- = when 



/- 0. 



(21) In Question 23, if L = 1-25 x 10~ 3 henry, all the other con- 

 ditions remaining the same, express v in terms of t. 



(25) In Question 23, if L == 8 x 10~ 3 henry, all the other con- 

 ditions remaining the same, express v in terms of t. 



(26) A straight steel rod of uniform circular section and 5 feet 

 long is found to deflect 1 inch under a central load of 20 Ib. when 

 tested as a beam simply supported at the ends. Determine the 

 critical load when the same rod is used as a vertical strut with 

 free ends. (U.L., 1910.) 



(27) A hollow cylindrical steel strut has to be designed for the 

 following conditions : length C feet, axial load 12 tons, ratio of 

 internal diameter to external diameter 0-8, factor of safety 10. 

 Determine the external diameter of the strut and the thickness 

 of the metal, if the ends of the strut are firmly built in. Use 

 the Rankine-Gordon formula, taking /-- 21 tons per sq. inch, 



and the constant for free ends as (U.L., 1908.) 



(28) A mild steel I joist, 9 inches deep over all, flanges 4-5 inches 

 wide by 0-5 inch thick, web 0-5 inch thick, is used as a column, 

 20 feet high, loaded centrally. If the ends are firmly fixed, find 

 the allowable load. Use the Rankine-Gordon formula ; take the 

 safe compressive stress as 12,000 Ib. per sq. inch and the coefficient 



for free ends as (U.L., 1909.) 



