369889
When a \(8\;kg\) mass is hung vertically on a light spring that obey's Hooke's law, the spring stretched by \(2\;cm\). The work required to be done by an external agent in stretching this spring by \(10\;cm\) will be
369890
A metallic rod of length \(l\) and cross-section area \(A\) is made of a material of Young modulus \(Y\). If the rod is elongated by an amount \(y\), then the work done is proportional to
1 \(\dfrac{1}{y}\)
2 \(y\)
3 \(\dfrac{1}{y^{2}}\)
4 \(y^{2}\)
Explanation:
\(V=A l\) Young's modulus \(Y=\dfrac{\text { Stress }}{\text { Strain }}\) Work done, \(W=\dfrac{1}{2} \times\) Stress \(\times\) Strain \(\times\) volume \(W = \frac{1}{2} \times Y \times {({\text{ Strain }})^2} \times Al\) \( = \frac{1}{2} \times Y \times {\left( {\frac{y}{l}} \right)^2} \times Al = \frac{1}{2}\left( {\frac{{YA}}{l}} \right){y^2} \Rightarrow W \propto {y^2}.\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369891
The elastic energy stored per unit volume in a stretched wire is
369892
The graph shows the behaviour of a wire in the region for which the substance obeys Hooke's Law. \(P\) and \(Q\) represent
1 \(P=\) Extension, \(Q=\) Applied force
2 \(P\) =Applied force, \(Q=\) Extension
3 \(P=\) Stored elastic energy, \(Q=\) Extension
4 \(P=\) Extension, \(Q=\) Stored elastic energy
Explanation:
Graph between applied force and extension will be straight line because in elastic range, \(F\,\alpha \,x\) The graph between extension and stored elastic energy will be parabolic in nature \({\text{As}}\,\,\,U = 1/2{\mkern 1mu} \,k{x^2}\;{\text{or}}\;U \propto {x^2}.\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369893
A wire of length \(L\) and cross-sectional area \(A\) is made of a material of Young's modulus \(Y\). It is stretched by an amount \(x\). The work done (or energy stored) is
1 \(\dfrac{Y x^{2} A}{L}\)
2 \(\dfrac{Y x A}{2 L}\)
3 \(\dfrac{2 Y x^{2} A}{L}\)
4 \(\dfrac{Y x^{2} A}{2 L}\)
Explanation:
We can treat the rod as a spring and its spring constant is \(K=\dfrac{Y A}{L}\) Work done in stretching the spring (rod) is \(W=\dfrac{1}{2} K x^{2}=\dfrac{Y A x^{2}}{2 L}\)
369889
When a \(8\;kg\) mass is hung vertically on a light spring that obey's Hooke's law, the spring stretched by \(2\;cm\). The work required to be done by an external agent in stretching this spring by \(10\;cm\) will be
369890
A metallic rod of length \(l\) and cross-section area \(A\) is made of a material of Young modulus \(Y\). If the rod is elongated by an amount \(y\), then the work done is proportional to
1 \(\dfrac{1}{y}\)
2 \(y\)
3 \(\dfrac{1}{y^{2}}\)
4 \(y^{2}\)
Explanation:
\(V=A l\) Young's modulus \(Y=\dfrac{\text { Stress }}{\text { Strain }}\) Work done, \(W=\dfrac{1}{2} \times\) Stress \(\times\) Strain \(\times\) volume \(W = \frac{1}{2} \times Y \times {({\text{ Strain }})^2} \times Al\) \( = \frac{1}{2} \times Y \times {\left( {\frac{y}{l}} \right)^2} \times Al = \frac{1}{2}\left( {\frac{{YA}}{l}} \right){y^2} \Rightarrow W \propto {y^2}.\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369891
The elastic energy stored per unit volume in a stretched wire is
369892
The graph shows the behaviour of a wire in the region for which the substance obeys Hooke's Law. \(P\) and \(Q\) represent
1 \(P=\) Extension, \(Q=\) Applied force
2 \(P\) =Applied force, \(Q=\) Extension
3 \(P=\) Stored elastic energy, \(Q=\) Extension
4 \(P=\) Extension, \(Q=\) Stored elastic energy
Explanation:
Graph between applied force and extension will be straight line because in elastic range, \(F\,\alpha \,x\) The graph between extension and stored elastic energy will be parabolic in nature \({\text{As}}\,\,\,U = 1/2{\mkern 1mu} \,k{x^2}\;{\text{or}}\;U \propto {x^2}.\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369893
A wire of length \(L\) and cross-sectional area \(A\) is made of a material of Young's modulus \(Y\). It is stretched by an amount \(x\). The work done (or energy stored) is
1 \(\dfrac{Y x^{2} A}{L}\)
2 \(\dfrac{Y x A}{2 L}\)
3 \(\dfrac{2 Y x^{2} A}{L}\)
4 \(\dfrac{Y x^{2} A}{2 L}\)
Explanation:
We can treat the rod as a spring and its spring constant is \(K=\dfrac{Y A}{L}\) Work done in stretching the spring (rod) is \(W=\dfrac{1}{2} K x^{2}=\dfrac{Y A x^{2}}{2 L}\)
369889
When a \(8\;kg\) mass is hung vertically on a light spring that obey's Hooke's law, the spring stretched by \(2\;cm\). The work required to be done by an external agent in stretching this spring by \(10\;cm\) will be
369890
A metallic rod of length \(l\) and cross-section area \(A\) is made of a material of Young modulus \(Y\). If the rod is elongated by an amount \(y\), then the work done is proportional to
1 \(\dfrac{1}{y}\)
2 \(y\)
3 \(\dfrac{1}{y^{2}}\)
4 \(y^{2}\)
Explanation:
\(V=A l\) Young's modulus \(Y=\dfrac{\text { Stress }}{\text { Strain }}\) Work done, \(W=\dfrac{1}{2} \times\) Stress \(\times\) Strain \(\times\) volume \(W = \frac{1}{2} \times Y \times {({\text{ Strain }})^2} \times Al\) \( = \frac{1}{2} \times Y \times {\left( {\frac{y}{l}} \right)^2} \times Al = \frac{1}{2}\left( {\frac{{YA}}{l}} \right){y^2} \Rightarrow W \propto {y^2}.\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369891
The elastic energy stored per unit volume in a stretched wire is
369892
The graph shows the behaviour of a wire in the region for which the substance obeys Hooke's Law. \(P\) and \(Q\) represent
1 \(P=\) Extension, \(Q=\) Applied force
2 \(P\) =Applied force, \(Q=\) Extension
3 \(P=\) Stored elastic energy, \(Q=\) Extension
4 \(P=\) Extension, \(Q=\) Stored elastic energy
Explanation:
Graph between applied force and extension will be straight line because in elastic range, \(F\,\alpha \,x\) The graph between extension and stored elastic energy will be parabolic in nature \({\text{As}}\,\,\,U = 1/2{\mkern 1mu} \,k{x^2}\;{\text{or}}\;U \propto {x^2}.\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369893
A wire of length \(L\) and cross-sectional area \(A\) is made of a material of Young's modulus \(Y\). It is stretched by an amount \(x\). The work done (or energy stored) is
1 \(\dfrac{Y x^{2} A}{L}\)
2 \(\dfrac{Y x A}{2 L}\)
3 \(\dfrac{2 Y x^{2} A}{L}\)
4 \(\dfrac{Y x^{2} A}{2 L}\)
Explanation:
We can treat the rod as a spring and its spring constant is \(K=\dfrac{Y A}{L}\) Work done in stretching the spring (rod) is \(W=\dfrac{1}{2} K x^{2}=\dfrac{Y A x^{2}}{2 L}\)
NEET Test Series from KOTA - 10 Papers In MS WORD
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PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369889
When a \(8\;kg\) mass is hung vertically on a light spring that obey's Hooke's law, the spring stretched by \(2\;cm\). The work required to be done by an external agent in stretching this spring by \(10\;cm\) will be
369890
A metallic rod of length \(l\) and cross-section area \(A\) is made of a material of Young modulus \(Y\). If the rod is elongated by an amount \(y\), then the work done is proportional to
1 \(\dfrac{1}{y}\)
2 \(y\)
3 \(\dfrac{1}{y^{2}}\)
4 \(y^{2}\)
Explanation:
\(V=A l\) Young's modulus \(Y=\dfrac{\text { Stress }}{\text { Strain }}\) Work done, \(W=\dfrac{1}{2} \times\) Stress \(\times\) Strain \(\times\) volume \(W = \frac{1}{2} \times Y \times {({\text{ Strain }})^2} \times Al\) \( = \frac{1}{2} \times Y \times {\left( {\frac{y}{l}} \right)^2} \times Al = \frac{1}{2}\left( {\frac{{YA}}{l}} \right){y^2} \Rightarrow W \propto {y^2}.\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369891
The elastic energy stored per unit volume in a stretched wire is
369892
The graph shows the behaviour of a wire in the region for which the substance obeys Hooke's Law. \(P\) and \(Q\) represent
1 \(P=\) Extension, \(Q=\) Applied force
2 \(P\) =Applied force, \(Q=\) Extension
3 \(P=\) Stored elastic energy, \(Q=\) Extension
4 \(P=\) Extension, \(Q=\) Stored elastic energy
Explanation:
Graph between applied force and extension will be straight line because in elastic range, \(F\,\alpha \,x\) The graph between extension and stored elastic energy will be parabolic in nature \({\text{As}}\,\,\,U = 1/2{\mkern 1mu} \,k{x^2}\;{\text{or}}\;U \propto {x^2}.\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369893
A wire of length \(L\) and cross-sectional area \(A\) is made of a material of Young's modulus \(Y\). It is stretched by an amount \(x\). The work done (or energy stored) is
1 \(\dfrac{Y x^{2} A}{L}\)
2 \(\dfrac{Y x A}{2 L}\)
3 \(\dfrac{2 Y x^{2} A}{L}\)
4 \(\dfrac{Y x^{2} A}{2 L}\)
Explanation:
We can treat the rod as a spring and its spring constant is \(K=\dfrac{Y A}{L}\) Work done in stretching the spring (rod) is \(W=\dfrac{1}{2} K x^{2}=\dfrac{Y A x^{2}}{2 L}\)
369889
When a \(8\;kg\) mass is hung vertically on a light spring that obey's Hooke's law, the spring stretched by \(2\;cm\). The work required to be done by an external agent in stretching this spring by \(10\;cm\) will be
369890
A metallic rod of length \(l\) and cross-section area \(A\) is made of a material of Young modulus \(Y\). If the rod is elongated by an amount \(y\), then the work done is proportional to
1 \(\dfrac{1}{y}\)
2 \(y\)
3 \(\dfrac{1}{y^{2}}\)
4 \(y^{2}\)
Explanation:
\(V=A l\) Young's modulus \(Y=\dfrac{\text { Stress }}{\text { Strain }}\) Work done, \(W=\dfrac{1}{2} \times\) Stress \(\times\) Strain \(\times\) volume \(W = \frac{1}{2} \times Y \times {({\text{ Strain }})^2} \times Al\) \( = \frac{1}{2} \times Y \times {\left( {\frac{y}{l}} \right)^2} \times Al = \frac{1}{2}\left( {\frac{{YA}}{l}} \right){y^2} \Rightarrow W \propto {y^2}.\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369891
The elastic energy stored per unit volume in a stretched wire is
369892
The graph shows the behaviour of a wire in the region for which the substance obeys Hooke's Law. \(P\) and \(Q\) represent
1 \(P=\) Extension, \(Q=\) Applied force
2 \(P\) =Applied force, \(Q=\) Extension
3 \(P=\) Stored elastic energy, \(Q=\) Extension
4 \(P=\) Extension, \(Q=\) Stored elastic energy
Explanation:
Graph between applied force and extension will be straight line because in elastic range, \(F\,\alpha \,x\) The graph between extension and stored elastic energy will be parabolic in nature \({\text{As}}\,\,\,U = 1/2{\mkern 1mu} \,k{x^2}\;{\text{or}}\;U \propto {x^2}.\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS
369893
A wire of length \(L\) and cross-sectional area \(A\) is made of a material of Young's modulus \(Y\). It is stretched by an amount \(x\). The work done (or energy stored) is
1 \(\dfrac{Y x^{2} A}{L}\)
2 \(\dfrac{Y x A}{2 L}\)
3 \(\dfrac{2 Y x^{2} A}{L}\)
4 \(\dfrac{Y x^{2} A}{2 L}\)
Explanation:
We can treat the rod as a spring and its spring constant is \(K=\dfrac{Y A}{L}\) Work done in stretching the spring (rod) is \(W=\dfrac{1}{2} K x^{2}=\dfrac{Y A x^{2}}{2 L}\)
