An $8\,m$ long copper wire and $4\,m$ long steel wire, each of cross section $0.5\,cm^2$ are fastened end to end and stretched by $500\,N$ force. The elastic potential energy of the system is (Youngs mod $: Y_{cu}= 1\times 10^{11}\,N/m^2,$ $Y_{steel} = 2\times 10^{11}\,N/m^2$ ) :
A$1/4\,\,J$
B$1/3\,\,J$
C$1/2\,\,J$
D$1\,\,J$
Diffcult
Download our app for free and get started
A$1/4\,\,J$
a Work $=$ Energy stored
$=\frac{1}{2} \times(\text { Force }) \times(\Delta l)$
Net $\Delta l=\Delta l_{1}+\Delta l_{2}=1 \mathrm{mm}=10^{-3} \mathrm{m}$
Elastic potential energy $=\frac{1}{2} \times 500 \times 10^{-3}=?$
$=\frac{1}{4} J$
Download our app
and get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
The following four wires of length $L$ and radius $r$ are made of the same material. Which of these will have the largest extension, when the same tension is applied?
A uniform metallic wire is elongated by $0.04\, m$ when subjected to a linear force $F$. The elongation, if its length and diameter is doubled and subjected to the same force will be ..... $cm .$
Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is $1: 4,$ the ratio of their diameters is
The ratio of Young's modulus of the material of two wires is $2 : 3.$ If the same stress is applied on both, then the ratio of elastic energy per unit volume will be
Two wires $A$ and $B$ of same material have radii in the ratio $2: 1$ and lengths in the ratio $4: 1$. The ratio of the normal forces required to produce the same change in the lengths of these two wires is .......
The upper end of a wire of radius $4\, mm$ and length $100\, cm$ is clamped and its other end is twisted through an angle of $60^o$. Then angle of shear is .......... $^o$
A force $F$ is applied on a square area of side $L$. If the percentage error in the measurement of $L$ is $2 \%$ and that in $F$ is $4 \%$, what is the maximum percentage error in pressure?