WORK - ENERGY THEOREM
Work, Energy and Power

268880 A lifting machine, having an efficiency of \(\mathbf{8 0 \%}\) uses \(2500 \mathrm{~J}\) of energy in lifting a \(10 \mathrm{~kg}\) load over a certain height. If the load is now allowed to fall through that height freely, its velocity at the end of the fall will be ( \(g=10 \mathrm{~m} / \mathrm{s}^{2}\) )

1 \(10 \mathrm{~m} \mathrm{~s}^{-1} 2\)
2 \(15 \mathrm{~m} \mathrm{~s}^{-1}\)
3 \(20 \mathrm{~m} \mathrm{~s}^{-1}\)
4 \(25 \mathrm{~m} \mathrm{~s}^{-1}\)
Work, Energy and Power

268881 A chain \(A B\) of length \(L\) is lying in a smooth horizontal tube so that a fraction \(h\) of its length L, hangs freely and touches the surface of the table with its end B. At a certain moment, the end \(A\) of the chain is set free. The velocity of end A of the chain, when it slips out of tube, is

1 \(h \sqrt{\frac{2 g}{L h}}\)
2 \(\sqrt{2 g h \log _{e} \boxminus \frac{L}{h}} \exists\)
3 \(\sqrt{2 g \log _{e} \boxminus \frac{L}{h} \theta}-\)
4 \(\frac{1}{h L} \sqrt{2 g}\)
Work, Energy and Power

268882 A block of mass \(m=1 \mathrm{~kg}\) moving on a horizontal surface with speed \(v_{i}=2 \mathrm{~ms}^{-1}\) enters a rough patch ranging from \(x=0.10 \mathrm{~m}\) to \(x=2.01 \mathrm{~m}\). The retarding force \(F_{r}=\frac{-k}{x}\) for \(0.1 \mathrm{~m}

1 \(.2 m s^{-1}\)
2 \(1 m^{-1}\)
3 \(3 m s^{-1}\)
4 \(0.5 \mathrm{~ms}^{-1}\)
Work, Energy and Power

268883 A \(1.5 \mathrm{~kg}\) block is initially at rest on a horizontal frictionless surface. A horizontal force \(\vec{F}=\left(4-x^{2}\right) \hat{i}\) is applied on the block . Initial position of the block is at \(x=0\). The maximum kinetic energy of the block between \(x=0\) and \(x=2 m\) is

1 \(2.33 \mathrm{~J}\)
2 \(8.67 \mathrm{~J}\)
3 \(5.33 \mathrm{~J}\)
4 \(6.67 \mathrm{~J}\)
Work, Energy and Power

268880 A lifting machine, having an efficiency of \(\mathbf{8 0 \%}\) uses \(2500 \mathrm{~J}\) of energy in lifting a \(10 \mathrm{~kg}\) load over a certain height. If the load is now allowed to fall through that height freely, its velocity at the end of the fall will be ( \(g=10 \mathrm{~m} / \mathrm{s}^{2}\) )

1 \(10 \mathrm{~m} \mathrm{~s}^{-1} 2\)
2 \(15 \mathrm{~m} \mathrm{~s}^{-1}\)
3 \(20 \mathrm{~m} \mathrm{~s}^{-1}\)
4 \(25 \mathrm{~m} \mathrm{~s}^{-1}\)
Work, Energy and Power

268881 A chain \(A B\) of length \(L\) is lying in a smooth horizontal tube so that a fraction \(h\) of its length L, hangs freely and touches the surface of the table with its end B. At a certain moment, the end \(A\) of the chain is set free. The velocity of end A of the chain, when it slips out of tube, is

1 \(h \sqrt{\frac{2 g}{L h}}\)
2 \(\sqrt{2 g h \log _{e} \boxminus \frac{L}{h}} \exists\)
3 \(\sqrt{2 g \log _{e} \boxminus \frac{L}{h} \theta}-\)
4 \(\frac{1}{h L} \sqrt{2 g}\)
Work, Energy and Power

268882 A block of mass \(m=1 \mathrm{~kg}\) moving on a horizontal surface with speed \(v_{i}=2 \mathrm{~ms}^{-1}\) enters a rough patch ranging from \(x=0.10 \mathrm{~m}\) to \(x=2.01 \mathrm{~m}\). The retarding force \(F_{r}=\frac{-k}{x}\) for \(0.1 \mathrm{~m}

1 \(.2 m s^{-1}\)
2 \(1 m^{-1}\)
3 \(3 m s^{-1}\)
4 \(0.5 \mathrm{~ms}^{-1}\)
Work, Energy and Power

268883 A \(1.5 \mathrm{~kg}\) block is initially at rest on a horizontal frictionless surface. A horizontal force \(\vec{F}=\left(4-x^{2}\right) \hat{i}\) is applied on the block . Initial position of the block is at \(x=0\). The maximum kinetic energy of the block between \(x=0\) and \(x=2 m\) is

1 \(2.33 \mathrm{~J}\)
2 \(8.67 \mathrm{~J}\)
3 \(5.33 \mathrm{~J}\)
4 \(6.67 \mathrm{~J}\)
Work, Energy and Power

268880 A lifting machine, having an efficiency of \(\mathbf{8 0 \%}\) uses \(2500 \mathrm{~J}\) of energy in lifting a \(10 \mathrm{~kg}\) load over a certain height. If the load is now allowed to fall through that height freely, its velocity at the end of the fall will be ( \(g=10 \mathrm{~m} / \mathrm{s}^{2}\) )

1 \(10 \mathrm{~m} \mathrm{~s}^{-1} 2\)
2 \(15 \mathrm{~m} \mathrm{~s}^{-1}\)
3 \(20 \mathrm{~m} \mathrm{~s}^{-1}\)
4 \(25 \mathrm{~m} \mathrm{~s}^{-1}\)
Work, Energy and Power

268881 A chain \(A B\) of length \(L\) is lying in a smooth horizontal tube so that a fraction \(h\) of its length L, hangs freely and touches the surface of the table with its end B. At a certain moment, the end \(A\) of the chain is set free. The velocity of end A of the chain, when it slips out of tube, is

1 \(h \sqrt{\frac{2 g}{L h}}\)
2 \(\sqrt{2 g h \log _{e} \boxminus \frac{L}{h}} \exists\)
3 \(\sqrt{2 g \log _{e} \boxminus \frac{L}{h} \theta}-\)
4 \(\frac{1}{h L} \sqrt{2 g}\)
Work, Energy and Power

268882 A block of mass \(m=1 \mathrm{~kg}\) moving on a horizontal surface with speed \(v_{i}=2 \mathrm{~ms}^{-1}\) enters a rough patch ranging from \(x=0.10 \mathrm{~m}\) to \(x=2.01 \mathrm{~m}\). The retarding force \(F_{r}=\frac{-k}{x}\) for \(0.1 \mathrm{~m}

1 \(.2 m s^{-1}\)
2 \(1 m^{-1}\)
3 \(3 m s^{-1}\)
4 \(0.5 \mathrm{~ms}^{-1}\)
Work, Energy and Power

268883 A \(1.5 \mathrm{~kg}\) block is initially at rest on a horizontal frictionless surface. A horizontal force \(\vec{F}=\left(4-x^{2}\right) \hat{i}\) is applied on the block . Initial position of the block is at \(x=0\). The maximum kinetic energy of the block between \(x=0\) and \(x=2 m\) is

1 \(2.33 \mathrm{~J}\)
2 \(8.67 \mathrm{~J}\)
3 \(5.33 \mathrm{~J}\)
4 \(6.67 \mathrm{~J}\)
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Work, Energy and Power

268880 A lifting machine, having an efficiency of \(\mathbf{8 0 \%}\) uses \(2500 \mathrm{~J}\) of energy in lifting a \(10 \mathrm{~kg}\) load over a certain height. If the load is now allowed to fall through that height freely, its velocity at the end of the fall will be ( \(g=10 \mathrm{~m} / \mathrm{s}^{2}\) )

1 \(10 \mathrm{~m} \mathrm{~s}^{-1} 2\)
2 \(15 \mathrm{~m} \mathrm{~s}^{-1}\)
3 \(20 \mathrm{~m} \mathrm{~s}^{-1}\)
4 \(25 \mathrm{~m} \mathrm{~s}^{-1}\)
Work, Energy and Power

268881 A chain \(A B\) of length \(L\) is lying in a smooth horizontal tube so that a fraction \(h\) of its length L, hangs freely and touches the surface of the table with its end B. At a certain moment, the end \(A\) of the chain is set free. The velocity of end A of the chain, when it slips out of tube, is

1 \(h \sqrt{\frac{2 g}{L h}}\)
2 \(\sqrt{2 g h \log _{e} \boxminus \frac{L}{h}} \exists\)
3 \(\sqrt{2 g \log _{e} \boxminus \frac{L}{h} \theta}-\)
4 \(\frac{1}{h L} \sqrt{2 g}\)
Work, Energy and Power

268882 A block of mass \(m=1 \mathrm{~kg}\) moving on a horizontal surface with speed \(v_{i}=2 \mathrm{~ms}^{-1}\) enters a rough patch ranging from \(x=0.10 \mathrm{~m}\) to \(x=2.01 \mathrm{~m}\). The retarding force \(F_{r}=\frac{-k}{x}\) for \(0.1 \mathrm{~m}

1 \(.2 m s^{-1}\)
2 \(1 m^{-1}\)
3 \(3 m s^{-1}\)
4 \(0.5 \mathrm{~ms}^{-1}\)
Work, Energy and Power

268883 A \(1.5 \mathrm{~kg}\) block is initially at rest on a horizontal frictionless surface. A horizontal force \(\vec{F}=\left(4-x^{2}\right) \hat{i}\) is applied on the block . Initial position of the block is at \(x=0\). The maximum kinetic energy of the block between \(x=0\) and \(x=2 m\) is

1 \(2.33 \mathrm{~J}\)
2 \(8.67 \mathrm{~J}\)
3 \(5.33 \mathrm{~J}\)
4 \(6.67 \mathrm{~J}\)