An iron rod of length 2m and cross-section area of $50 mm^2$ stretched by 0.5 mm, when a mass of 250 kg is hung from its lower end. What is young's modulus of the iron rod ?
$ Y = { MgL \over Al } $
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An iron rod of length 2m and cross-section area of $50 mm^2$ stretched by 0.5 mm, when a mass of 250 kg is hung from its lower end. What is young's modulus of the iron rod ?
$ Y = { MgL \over Al } $
A load W produces an extension of 1mm in a thread of radius r. Now if the load is made 4 w and radius is made 2r all other things remaining same the extension will becomes..............
$ l = { FL \over AY} $ $ \therefore l \alpha {F \over r^2 } $
A steel wire of 1m long and $1mm^2$ cross sectional area is hung from rigid end when weight of 1 kg is hung from it then change in length will be ……$ ( Y = 2 \times 10 ^{11} N/m^2 ) $
$ L = { mgL \over AY } $
Calculate the work done, if wire is loaded by 'M g' weight and the increase in length is 'l' ?
$ work done = { 1 \over 2 } Fl = { Mgl\ove r2 } $
Two wires of same diameter of the same material having the length l and 2 l . If the force F is applied on each, what will be the ratio of the work done in the two wires ?
$ w = { 1 \over 2} { (stress)^2 \over Y } \times volume $ $ As F, Aand Y are same - W \alpha volume (area is same)$ $ w \alpha l $ (v =A1) $ { w_1 \over w_2 } = { l_1 \over l_2 } = { l_1 \over 2 l } = {1 \over 2} $
A 5 meter long wire is fixed to the ceiling. A weight of 10 kg is hung at the lower end and is 1 meter above the four. The wire was elongated by 1 mm. What is the stored in the wire due to stretching ?
$ { w = {1 \over 2 } \times F \times l $
If the force constant of a wire is k. What is the work done in increasing the length of the wire by l ?
$ K = {F \over l } and w = { 1 \over 2 } F l = {1 \over 2 } kl \times l = {1 \over 2 } kl^2 $
Wire A and B are made from the same material. A has twice the diameter and three times the length of B. If the elastic limits are not reached when each is stretched by the same tension, what is the ratio of energy stored in A to that in B ?
$ U = { 1 \over 2} Fl = { F^2 l \over 2 AY } ; U \alpha {L \over r^2 } (F and Y are constant ) $
A wire suspended vertically from one of its ends is stretched by attaching a weight of 200 N to the lower and. The weight stretches the wire by 1 mm. Then what is the elastic energy stored in the wire ?
$ U = {1 \over 2 } Fl $
A brass rod of cross sectional area 1 cm2 and length 0.2 mis compressed length wise by a weight of 5 kg. If young's modulus of elasticity of brass is $ 1 \times 10 ^ {11} N /m^2 $ and $ g = 10 m/s^2 $ . Then what will be increase in the energy of rod ?
$ U = {1 \over 2} \times {(stress )^2 \over Y } \times volume $
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