A bar of length 1 m is supported at its two ends. The breadth and depth of the bar are 5 cm and 0.5 cm., respectively , A body of mass 0.1 is suspended at the centre of the bar. Calculate the depression produced in the bar.

Explanation

Data : L = 1 m, b = 5 cm = ` 5 xx 10^(-2) m .d = 0.5 cm = 5 xx 10^(-3) ` m
`M = 0.1 kg, Y = 2 xx 10^(11) N//m^(2)`
Load , W = Mg = ` 0.1 xx 9.8 = 0.98 N`
The depression (sag) produced in the bar.
` delta = W/(4by) (l/d)^(3) = 0.98/(4 (5 xx 10^(-2)) (2xx 10^(11)) . (1/(5 xx 10^(-3)))^(3)`
` = 0.98/(4xx 10^(16) . (2 xx 10^(2))^(3) = (0.98 xx 8 xx 10^(6))/( 4 xx 10^(10)) = 1.96 xx 10^(-4) m = 0.196 mm`