Vertical Circular Motion
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PHXI06:WORK ENERGY AND POWER

355727 A bob of mass \(M\) is suspended by a massless string of length \(L\). The horizontal velocity \(V\) at position \(A\) is just sufficient to make it reach the point \(B\). The angle \(\theta\) at which the speed of the bob is half of that at \(A\), satisfies
supporting img

1 \(\theta=\dfrac{\pi}{4}\)
2 \(\dfrac{\pi}{4} < \theta < \dfrac{\pi}{2}\)
3 \(\dfrac{\pi}{2} < \theta < \dfrac{3 \pi}{4}\)
4 \(\dfrac{3 \pi}{4} < \theta < \pi\)
PHXI06:WORK ENERGY AND POWER

355728 A mass \(m\) starting from \(A\) reaches \(B\) of a frictionless track. On reaching \(B\), it pushes the track with a force equal to \(\mathrm{x}\) times its weight, then the applicable relation is
supporting img

1 \(h=\dfrac{(x+5)}{2} r\)
2 \(h=\dfrac{x}{2} r\)
3 \(h=r\)
4 \(h=\left(\dfrac{x+1}{2}\right) r\)
PHXI06:WORK ENERGY AND POWER

355729 A particle is given an initial speed \(u\) inside a smooth spherical shell of radius \(R = 2\;m\) so that it just completes a circle. Acceleration of the particle when it is in vertical circle is \((g = 10\;m{\rm{/}}{s^2},\sqrt {10} = 3.16)\)
supporting img

1 \(31.6\,m/{s^2}\)
2 \(11.25\,m/{s^2}\)
3 \(27.3\,\,m/{s^2}\)
4 \(42.7\,\,m/{s^2}\)
PHXI06:WORK ENERGY AND POWER

355730 A stone of mass \(m\) is tied to a string and is moved in a vertical circle of radius \(r\) making \(n\,rev{\rm{/}}\min \). The total tension in the string when the stone is at the lowest point is

1 \(m g\)
2 \(m\left(g+\pi n r^{2}\right)\)
3 \(m(g+n r)\)
4 \(m\left(g+\dfrac{\pi^{2} n^{2} r}{900}\right)\)
PHXI06:WORK ENERGY AND POWER

355731 A sphere is suspended by a thread of length \(l\). What minimum horizontal velocity has to be imparted to the ball for it to reach the height of the suspension?

1 \(g l\)
2 \(\sqrt{2 g l}\)
3 \(2 g l\)
4 \(\sqrt{g l}\)
NEET DIGITAL LIBRARY
PHXI06:WORK ENERGY AND POWER

355727 A bob of mass \(M\) is suspended by a massless string of length \(L\). The horizontal velocity \(V\) at position \(A\) is just sufficient to make it reach the point \(B\). The angle \(\theta\) at which the speed of the bob is half of that at \(A\), satisfies
supporting img

1 \(\theta=\dfrac{\pi}{4}\)
2 \(\dfrac{\pi}{4} < \theta < \dfrac{\pi}{2}\)
3 \(\dfrac{\pi}{2} < \theta < \dfrac{3 \pi}{4}\)
4 \(\dfrac{3 \pi}{4} < \theta < \pi\)
PHXI06:WORK ENERGY AND POWER

355728 A mass \(m\) starting from \(A\) reaches \(B\) of a frictionless track. On reaching \(B\), it pushes the track with a force equal to \(\mathrm{x}\) times its weight, then the applicable relation is
supporting img

1 \(h=\dfrac{(x+5)}{2} r\)
2 \(h=\dfrac{x}{2} r\)
3 \(h=r\)
4 \(h=\left(\dfrac{x+1}{2}\right) r\)
PHXI06:WORK ENERGY AND POWER

355729 A particle is given an initial speed \(u\) inside a smooth spherical shell of radius \(R = 2\;m\) so that it just completes a circle. Acceleration of the particle when it is in vertical circle is \((g = 10\;m{\rm{/}}{s^2},\sqrt {10} = 3.16)\)
supporting img

1 \(31.6\,m/{s^2}\)
2 \(11.25\,m/{s^2}\)
3 \(27.3\,\,m/{s^2}\)
4 \(42.7\,\,m/{s^2}\)
PHXI06:WORK ENERGY AND POWER

355730 A stone of mass \(m\) is tied to a string and is moved in a vertical circle of radius \(r\) making \(n\,rev{\rm{/}}\min \). The total tension in the string when the stone is at the lowest point is

1 \(m g\)
2 \(m\left(g+\pi n r^{2}\right)\)
3 \(m(g+n r)\)
4 \(m\left(g+\dfrac{\pi^{2} n^{2} r}{900}\right)\)
PHXI06:WORK ENERGY AND POWER

355731 A sphere is suspended by a thread of length \(l\). What minimum horizontal velocity has to be imparted to the ball for it to reach the height of the suspension?

1 \(g l\)
2 \(\sqrt{2 g l}\)
3 \(2 g l\)
4 \(\sqrt{g l}\)
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PHXI06:WORK ENERGY AND POWER

355727 A bob of mass \(M\) is suspended by a massless string of length \(L\). The horizontal velocity \(V\) at position \(A\) is just sufficient to make it reach the point \(B\). The angle \(\theta\) at which the speed of the bob is half of that at \(A\), satisfies
supporting img

1 \(\theta=\dfrac{\pi}{4}\)
2 \(\dfrac{\pi}{4} < \theta < \dfrac{\pi}{2}\)
3 \(\dfrac{\pi}{2} < \theta < \dfrac{3 \pi}{4}\)
4 \(\dfrac{3 \pi}{4} < \theta < \pi\)
PHXI06:WORK ENERGY AND POWER

355728 A mass \(m\) starting from \(A\) reaches \(B\) of a frictionless track. On reaching \(B\), it pushes the track with a force equal to \(\mathrm{x}\) times its weight, then the applicable relation is
supporting img

1 \(h=\dfrac{(x+5)}{2} r\)
2 \(h=\dfrac{x}{2} r\)
3 \(h=r\)
4 \(h=\left(\dfrac{x+1}{2}\right) r\)
PHXI06:WORK ENERGY AND POWER

355729 A particle is given an initial speed \(u\) inside a smooth spherical shell of radius \(R = 2\;m\) so that it just completes a circle. Acceleration of the particle when it is in vertical circle is \((g = 10\;m{\rm{/}}{s^2},\sqrt {10} = 3.16)\)
supporting img

1 \(31.6\,m/{s^2}\)
2 \(11.25\,m/{s^2}\)
3 \(27.3\,\,m/{s^2}\)
4 \(42.7\,\,m/{s^2}\)
PHXI06:WORK ENERGY AND POWER

355730 A stone of mass \(m\) is tied to a string and is moved in a vertical circle of radius \(r\) making \(n\,rev{\rm{/}}\min \). The total tension in the string when the stone is at the lowest point is

1 \(m g\)
2 \(m\left(g+\pi n r^{2}\right)\)
3 \(m(g+n r)\)
4 \(m\left(g+\dfrac{\pi^{2} n^{2} r}{900}\right)\)
PHXI06:WORK ENERGY AND POWER

355731 A sphere is suspended by a thread of length \(l\). What minimum horizontal velocity has to be imparted to the ball for it to reach the height of the suspension?

1 \(g l\)
2 \(\sqrt{2 g l}\)
3 \(2 g l\)
4 \(\sqrt{g l}\)
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PHXI06:WORK ENERGY AND POWER

355727 A bob of mass \(M\) is suspended by a massless string of length \(L\). The horizontal velocity \(V\) at position \(A\) is just sufficient to make it reach the point \(B\). The angle \(\theta\) at which the speed of the bob is half of that at \(A\), satisfies
supporting img

1 \(\theta=\dfrac{\pi}{4}\)
2 \(\dfrac{\pi}{4} < \theta < \dfrac{\pi}{2}\)
3 \(\dfrac{\pi}{2} < \theta < \dfrac{3 \pi}{4}\)
4 \(\dfrac{3 \pi}{4} < \theta < \pi\)
PHXI06:WORK ENERGY AND POWER

355728 A mass \(m\) starting from \(A\) reaches \(B\) of a frictionless track. On reaching \(B\), it pushes the track with a force equal to \(\mathrm{x}\) times its weight, then the applicable relation is
supporting img

1 \(h=\dfrac{(x+5)}{2} r\)
2 \(h=\dfrac{x}{2} r\)
3 \(h=r\)
4 \(h=\left(\dfrac{x+1}{2}\right) r\)
PHXI06:WORK ENERGY AND POWER

355729 A particle is given an initial speed \(u\) inside a smooth spherical shell of radius \(R = 2\;m\) so that it just completes a circle. Acceleration of the particle when it is in vertical circle is \((g = 10\;m{\rm{/}}{s^2},\sqrt {10} = 3.16)\)
supporting img

1 \(31.6\,m/{s^2}\)
2 \(11.25\,m/{s^2}\)
3 \(27.3\,\,m/{s^2}\)
4 \(42.7\,\,m/{s^2}\)
PHXI06:WORK ENERGY AND POWER

355730 A stone of mass \(m\) is tied to a string and is moved in a vertical circle of radius \(r\) making \(n\,rev{\rm{/}}\min \). The total tension in the string when the stone is at the lowest point is

1 \(m g\)
2 \(m\left(g+\pi n r^{2}\right)\)
3 \(m(g+n r)\)
4 \(m\left(g+\dfrac{\pi^{2} n^{2} r}{900}\right)\)
PHXI06:WORK ENERGY AND POWER

355731 A sphere is suspended by a thread of length \(l\). What minimum horizontal velocity has to be imparted to the ball for it to reach the height of the suspension?

1 \(g l\)
2 \(\sqrt{2 g l}\)
3 \(2 g l\)
4 \(\sqrt{g l}\)
NEET DIGITAL LIBRARY
PHXI06:WORK ENERGY AND POWER

355727 A bob of mass \(M\) is suspended by a massless string of length \(L\). The horizontal velocity \(V\) at position \(A\) is just sufficient to make it reach the point \(B\). The angle \(\theta\) at which the speed of the bob is half of that at \(A\), satisfies
supporting img

1 \(\theta=\dfrac{\pi}{4}\)
2 \(\dfrac{\pi}{4} < \theta < \dfrac{\pi}{2}\)
3 \(\dfrac{\pi}{2} < \theta < \dfrac{3 \pi}{4}\)
4 \(\dfrac{3 \pi}{4} < \theta < \pi\)
PHXI06:WORK ENERGY AND POWER

355728 A mass \(m\) starting from \(A\) reaches \(B\) of a frictionless track. On reaching \(B\), it pushes the track with a force equal to \(\mathrm{x}\) times its weight, then the applicable relation is
supporting img

1 \(h=\dfrac{(x+5)}{2} r\)
2 \(h=\dfrac{x}{2} r\)
3 \(h=r\)
4 \(h=\left(\dfrac{x+1}{2}\right) r\)
PHXI06:WORK ENERGY AND POWER

355729 A particle is given an initial speed \(u\) inside a smooth spherical shell of radius \(R = 2\;m\) so that it just completes a circle. Acceleration of the particle when it is in vertical circle is \((g = 10\;m{\rm{/}}{s^2},\sqrt {10} = 3.16)\)
supporting img

1 \(31.6\,m/{s^2}\)
2 \(11.25\,m/{s^2}\)
3 \(27.3\,\,m/{s^2}\)
4 \(42.7\,\,m/{s^2}\)
PHXI06:WORK ENERGY AND POWER

355730 A stone of mass \(m\) is tied to a string and is moved in a vertical circle of radius \(r\) making \(n\,rev{\rm{/}}\min \). The total tension in the string when the stone is at the lowest point is

1 \(m g\)
2 \(m\left(g+\pi n r^{2}\right)\)
3 \(m(g+n r)\)
4 \(m\left(g+\dfrac{\pi^{2} n^{2} r}{900}\right)\)
PHXI06:WORK ENERGY AND POWER

355731 A sphere is suspended by a thread of length \(l\). What minimum horizontal velocity has to be imparted to the ball for it to reach the height of the suspension?

1 \(g l\)
2 \(\sqrt{2 g l}\)
3 \(2 g l\)
4 \(\sqrt{g l}\)