Question

Each of the three blocks P, Q and R shown in figure has a mass of 3 kg. Easch of the wires A and B has cross sectional area 0.005 cm^2 and Young modulus `2x10^11Nm^-2`. Neglect friction. Find the longitudinal strain developed ineach of the wires. Take `g=10ms^-2`

A. `500`
B. `1000`
C. `2000`
D. `3000`

Answer 1

Correct Answer - B

From force diagram, `T = 3a`......(i),
`T_(1) - T = 3a`........(ii) `3g - T_(1) = 3a`.......(iii)
After solving eqs. (i),(ii)
`:.` Stress `= (T)/(A) = (10)/(0.005xx10^(-4))`
`therefore` The elastic energy stored per unit volume
`= (1)/(2) xx "stress" xx "strain"`
`= (1)/(2) xx "stress" xx ("stress")/(Y) (because Y = ("Stress")/("Strain"))`
`= (Stress"^(2))/(2Y) = (((10)/(0.05xx10^(-4)))^(2))/(2xx2xx10^(11)), = 1000J//m^(3)`