NEET Physics Questions: Mechanical Properties of Solids

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The dimensions of four wires of the same material are given below, in which wire the increase in length will be maximum when the same strain is applied.




$ Y = { F \over A} { L \over l} \Rightarrow l \alpha { l \over A } \alpha {L \over \pi d^2 } $ $ \therefore l \alpha { L \over d^2 } ( As F and Y are constant ) $ The ratio of $ { L \over d^2 } $ is maximum for case CD
On increasing the length by 0.5 mm in a steel wire of length 2 mand area of cross-section $2 mm^2$ the force required is..............$ [ Y for steel = 2.2 \times 10^{11} N/m ] $




$ F = { YAI \over L } $
A stress of $ 3.8 \times 10^8 N m^2 $ is applied to steel rod of length 1 m along its length. Its young's modulus is $ 2 \times 10^ {11} N / m^2 0$. Then what is the elongation produced in the rod in mm ?




$ = { { F \over A} \over {\triangle l \over l} } $ $ given stress 3.18 \times 10^8 N/m^2 $ $ \therefore \triangle l ={ \triangle F /A \over Y } $
A force F is needed to break a copper wire having radius R, The force needed to break a copper wire of radius 2R will be........




Breaking force $ \alpha $ area of crossection of $( \pi r^2 ) $ wire If radius of wire is doubled then breaking force will become four times.
A rubber cord 10m long is suspended vertically. How much does it stretch under its own weight. $( Density of rubber is1500 kg /m^3 , Y = 5 \times 10^ 8 N /m^2 , g = 10 m/s ) $




$ l = { L^2 \over 2 Y } $
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If x, longitudinal strain is produced in a wire of young's modulus y then energy stored in the material of the wire per unit volume is..........




Energy stored per unit volume $ = {1 \over 2 } \times stress \times strain $
A steel wire of cross-sectional area $ 3 \times 10^ {-6} m^2 $ can with stand a maximum strain of $ 10 ^ {-3} $ Young's modulus of steel is $ 2 \times 10 ^ {11} N /m^2 $ . The maximum mass the wire can hold is ........$ ( g = 10 m/s^2 ) $




$ Y = { stress \over strain } \Rightarrow Max.strain = { Max.stress \over V}$ $ Max. strain = { mg /A \over Y } $
The young's modulus of a rubber string 8 cm long and density $ 1.5 kg /m^3 $ is $ 5 \times 10^8 N /m^2 $ .What will be the length increase due to its own weight?




$ l = { L^2 dg \over 2 Y } = { (8 \times 10^{-2} )^2 \times 1.5 \times 9.8 \over 2 \times 5 \times 10^8 } = 9.6 \times 10^{-11} m $
A and B are two wires. The radius of A is twice that of B. They are stretched by the same load. Then what is the stress on B ?




$ stress = { force \over area } \Rightarrow \therefore stress \alpha { 1 \over \pi r^2 } $ $ \therefore { S_B \over S_A} = \left( rA \over rB \right) ^2 = (2)^2 \Rightarrow S_B = $ S_A $
If the length of wire is reduced to half then it can hold the .........load.




Breaking force $ \alpha $ area of cross section of wire. i.e. load hold by the wire does not depend upon the length of the wire.
There are two wires of same material and same length. While the diameter of second wire is 2 times, the diameter of first wire. Then what will be the ratio of extension produced in the wire by applying same load ?




$ l = {FL \over AY} $ $ \therefore l \alpha { 1 \over r^2} $ ( F,L and Y are constant )
When the length of a wire having cross-section area $ 10 ^{-6} m^ 2 $ is stretched by 0.1% then tension in it is 100 N. Young's modulus of material of wire is...........




$ A = 10 ^ {-6} m^2 , Y = { {I \over A} \over { \triangle l \over l } } $
Two wires of equal lengths are made of the same material wire A has a diameter that is twice as that of wire B. If identical weights are suspended from the ends of these wires the increase in length is............




$ l = {FL \over AY } \Rightarrow l \alpha { 1 \over r^2} $ ( F,L and Y are constant)
Steel and copper wires of same length are stretched by the same weight one after the other. Young's modulus of steel the ratio increase in length ?




$ l = { FL \over AY} \Rightarrow { l_{steel} \over l_{a_1} } = { Ya_1 \over Y_{steel} } $ ( F,L and Y are constant )
A substance breaks down by a stress of If the density of the material of the wire is then the length of wire of the substance which will break under its own weight when suspended vertically is............




L = P /dg