369887
A wire of length ' \(L\) ' and area of cross section ' \(A\) ' is made of material of Young's modulus ' \(Y\) '. It is stretched by an amount ' \(x\) '. The work done in stretching the wire is
1 \(\dfrac{Y x^{2} A}{2 L}\)
2 \(\dfrac{2 Y x^{2} A}{L}\)
3 \(\dfrac{Y x A}{2 L}\)
4 \(\dfrac{Y x^{2} A}{2}\)
Explanation:
Force F required to stretch the wire by an amount l is given by \(F = \frac{{YA}}{L}l\) \(\therefore \) The work done in stretching the wire for a total extension of \(x\) is, \(W = \int_0^x {F.dl = \int_0^x {\frac{{YA}}{L}ldl = \frac{{YA}}{L}\left[ {\frac{{{l^2}}}{2}} \right]_0^x} } \) \( \Rightarrow W = \frac{{YA{x^2}}}{{2L}}\)
MHTCET - 2019
PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369888
Find the ratio of Young's modulus of wire \(A\) to wire \(B\)
369887
A wire of length ' \(L\) ' and area of cross section ' \(A\) ' is made of material of Young's modulus ' \(Y\) '. It is stretched by an amount ' \(x\) '. The work done in stretching the wire is
1 \(\dfrac{Y x^{2} A}{2 L}\)
2 \(\dfrac{2 Y x^{2} A}{L}\)
3 \(\dfrac{Y x A}{2 L}\)
4 \(\dfrac{Y x^{2} A}{2}\)
Explanation:
Force F required to stretch the wire by an amount l is given by \(F = \frac{{YA}}{L}l\) \(\therefore \) The work done in stretching the wire for a total extension of \(x\) is, \(W = \int_0^x {F.dl = \int_0^x {\frac{{YA}}{L}ldl = \frac{{YA}}{L}\left[ {\frac{{{l^2}}}{2}} \right]_0^x} } \) \( \Rightarrow W = \frac{{YA{x^2}}}{{2L}}\)
MHTCET - 2019
PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369888
Find the ratio of Young's modulus of wire \(A\) to wire \(B\)
