Conservation of Mechanical Energy
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PHXI06:WORK ENERGY AND POWER

355346 A ball is placed on a massless spring that is held at an angle of \(\theta\) with respect to the horizontal. The spring is then compressed a distance of \(x\) and released. When the ball reaches the maximum height of its trajectory, it is travelling at a speed \(v\). Then a different ball, weighing four as much as the first, is placed on the spring which is still at an angle \(\theta\). The spring is again compressed at a distance and released. Compared to the first ball, the second ball reaches a maximum height that is

1 4 times higher
2 \(\sin ^{2} \theta\) times as high
3 \(\dfrac{v^{2} g}{x}\) times as high
4 \(1 / 4\) times as high
PHXI06:WORK ENERGY AND POWER

355347 For a body thrown vertically upwards, its direction of motion changes at the point where its total mechanical energy is

1 Greater than the potential energy
2 Less than the potential energy
3 Equal to the potential energy
4 Zero
PHXI06:WORK ENERGY AND POWER

355348 A smooth chain \(PQ\) of mass \(M\) rests against \(a \dfrac{1}{4}\) th circular and smooth surface of radius \(r\). If released, its velocity to come over the horizontal part of the surface is
supporting img

1 \(\sqrt{2 g r\left(1-\dfrac{2}{\pi}\right)}\)
2 \(\sqrt {gr\left( {1 - \frac{2}{\pi }} \right)} \)
3 \(\sqrt{2 g r} \times \dfrac{1}{4}\)
4 \(\sqrt{2 g r\left(1-\dfrac{1}{\pi}\right)}\)
PHXI06:WORK ENERGY AND POWER

355349 A slab \(S\) of mass \(m\) is released from a height \(h_{0}\) from the top of a spring of force constant \(k\). The maximum compression \(x\) of the spring is given by the equation
supporting img

1 \(m g\left(h_{0}+x\right)=\dfrac{1}{2} k x^{2}\)
2 \(m g h_{0}=\dfrac{1}{2} k x^{2}\)
3 \(m g\left(h_{0}-x\right)=\dfrac{1}{2} k x^{2}\)
4 \(m g=h_{0} \dfrac{1}{2} k\left(h_{0}+x\right)^{2}\)
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PHXI06:WORK ENERGY AND POWER

355346 A ball is placed on a massless spring that is held at an angle of \(\theta\) with respect to the horizontal. The spring is then compressed a distance of \(x\) and released. When the ball reaches the maximum height of its trajectory, it is travelling at a speed \(v\). Then a different ball, weighing four as much as the first, is placed on the spring which is still at an angle \(\theta\). The spring is again compressed at a distance and released. Compared to the first ball, the second ball reaches a maximum height that is

1 4 times higher
2 \(\sin ^{2} \theta\) times as high
3 \(\dfrac{v^{2} g}{x}\) times as high
4 \(1 / 4\) times as high
PHXI06:WORK ENERGY AND POWER

355347 For a body thrown vertically upwards, its direction of motion changes at the point where its total mechanical energy is

1 Greater than the potential energy
2 Less than the potential energy
3 Equal to the potential energy
4 Zero
PHXI06:WORK ENERGY AND POWER

355348 A smooth chain \(PQ\) of mass \(M\) rests against \(a \dfrac{1}{4}\) th circular and smooth surface of radius \(r\). If released, its velocity to come over the horizontal part of the surface is
supporting img

1 \(\sqrt{2 g r\left(1-\dfrac{2}{\pi}\right)}\)
2 \(\sqrt {gr\left( {1 - \frac{2}{\pi }} \right)} \)
3 \(\sqrt{2 g r} \times \dfrac{1}{4}\)
4 \(\sqrt{2 g r\left(1-\dfrac{1}{\pi}\right)}\)
PHXI06:WORK ENERGY AND POWER

355349 A slab \(S\) of mass \(m\) is released from a height \(h_{0}\) from the top of a spring of force constant \(k\). The maximum compression \(x\) of the spring is given by the equation
supporting img

1 \(m g\left(h_{0}+x\right)=\dfrac{1}{2} k x^{2}\)
2 \(m g h_{0}=\dfrac{1}{2} k x^{2}\)
3 \(m g\left(h_{0}-x\right)=\dfrac{1}{2} k x^{2}\)
4 \(m g=h_{0} \dfrac{1}{2} k\left(h_{0}+x\right)^{2}\)
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PHXI06:WORK ENERGY AND POWER

355346 A ball is placed on a massless spring that is held at an angle of \(\theta\) with respect to the horizontal. The spring is then compressed a distance of \(x\) and released. When the ball reaches the maximum height of its trajectory, it is travelling at a speed \(v\). Then a different ball, weighing four as much as the first, is placed on the spring which is still at an angle \(\theta\). The spring is again compressed at a distance and released. Compared to the first ball, the second ball reaches a maximum height that is

1 4 times higher
2 \(\sin ^{2} \theta\) times as high
3 \(\dfrac{v^{2} g}{x}\) times as high
4 \(1 / 4\) times as high
PHXI06:WORK ENERGY AND POWER

355347 For a body thrown vertically upwards, its direction of motion changes at the point where its total mechanical energy is

1 Greater than the potential energy
2 Less than the potential energy
3 Equal to the potential energy
4 Zero
PHXI06:WORK ENERGY AND POWER

355348 A smooth chain \(PQ\) of mass \(M\) rests against \(a \dfrac{1}{4}\) th circular and smooth surface of radius \(r\). If released, its velocity to come over the horizontal part of the surface is
supporting img

1 \(\sqrt{2 g r\left(1-\dfrac{2}{\pi}\right)}\)
2 \(\sqrt {gr\left( {1 - \frac{2}{\pi }} \right)} \)
3 \(\sqrt{2 g r} \times \dfrac{1}{4}\)
4 \(\sqrt{2 g r\left(1-\dfrac{1}{\pi}\right)}\)
PHXI06:WORK ENERGY AND POWER

355349 A slab \(S\) of mass \(m\) is released from a height \(h_{0}\) from the top of a spring of force constant \(k\). The maximum compression \(x\) of the spring is given by the equation
supporting img

1 \(m g\left(h_{0}+x\right)=\dfrac{1}{2} k x^{2}\)
2 \(m g h_{0}=\dfrac{1}{2} k x^{2}\)
3 \(m g\left(h_{0}-x\right)=\dfrac{1}{2} k x^{2}\)
4 \(m g=h_{0} \dfrac{1}{2} k\left(h_{0}+x\right)^{2}\)
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PHXI06:WORK ENERGY AND POWER

355346 A ball is placed on a massless spring that is held at an angle of \(\theta\) with respect to the horizontal. The spring is then compressed a distance of \(x\) and released. When the ball reaches the maximum height of its trajectory, it is travelling at a speed \(v\). Then a different ball, weighing four as much as the first, is placed on the spring which is still at an angle \(\theta\). The spring is again compressed at a distance and released. Compared to the first ball, the second ball reaches a maximum height that is

1 4 times higher
2 \(\sin ^{2} \theta\) times as high
3 \(\dfrac{v^{2} g}{x}\) times as high
4 \(1 / 4\) times as high
PHXI06:WORK ENERGY AND POWER

355347 For a body thrown vertically upwards, its direction of motion changes at the point where its total mechanical energy is

1 Greater than the potential energy
2 Less than the potential energy
3 Equal to the potential energy
4 Zero
PHXI06:WORK ENERGY AND POWER

355348 A smooth chain \(PQ\) of mass \(M\) rests against \(a \dfrac{1}{4}\) th circular and smooth surface of radius \(r\). If released, its velocity to come over the horizontal part of the surface is
supporting img

1 \(\sqrt{2 g r\left(1-\dfrac{2}{\pi}\right)}\)
2 \(\sqrt {gr\left( {1 - \frac{2}{\pi }} \right)} \)
3 \(\sqrt{2 g r} \times \dfrac{1}{4}\)
4 \(\sqrt{2 g r\left(1-\dfrac{1}{\pi}\right)}\)
PHXI06:WORK ENERGY AND POWER

355349 A slab \(S\) of mass \(m\) is released from a height \(h_{0}\) from the top of a spring of force constant \(k\). The maximum compression \(x\) of the spring is given by the equation
supporting img

1 \(m g\left(h_{0}+x\right)=\dfrac{1}{2} k x^{2}\)
2 \(m g h_{0}=\dfrac{1}{2} k x^{2}\)
3 \(m g\left(h_{0}-x\right)=\dfrac{1}{2} k x^{2}\)
4 \(m g=h_{0} \dfrac{1}{2} k\left(h_{0}+x\right)^{2}\)
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