$A$ particle of mass $m$ is released from $a$ height $H$ on $a$ smooth curved surface which ends into a vertical loop of radius $R$, as shown The minimum value of $H$ required so that the particle makes a complete vertical circle is given by
$A$ particle of mass $m$ is released from $a$ height $H$ on $a$ smooth curved surface which ends into a vertical loop of radius $R$, as shown The minimum value of $H$ required so that the particle makes a complete vertical circle is given by
- A
$5 \,R$
- B
$4\, R$
- C
$2.5\, R$
- D
$2\, R$
Similar Questions
Two identical $5\,\,kg.$ blocks are moving with same speed of $2\,\,m/s$ towards each other along a frictionless horizontal surface. The two blocks collide, stick together and come to rest. Consider to two blocks as a system, the work done on the system by the external forces will be .............. $\mathrm{Joule}$
Two identical $5\,\,kg.$ blocks are moving with same speed of $2\,\,m/s$ towards each other along a frictionless horizontal surface. The two blocks collide, stick together and come to rest. Consider to two blocks as a system, the work done on the system by the external forces will be .............. $\mathrm{Joule}$
A particle moves with a velocity $\vec v\, = \,5\hat i - 3\hat j + 6\hat k\,\,m/s$ under the influence of a constant force $\vec F\, = \,10\hat i + 10\hat j + 20\hat k$. Instantaenous power will be ............... $\mathrm{J} / \mathrm{s}$
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A uniform flexible chain of mass $m$ and length $2l$ hangs in equilibrium over a smooth horizontal pin of negligible diameter. One end of the chain is given a small vertical displacement so that the chain slips over the pin. The speed of chain when it leaves pin is
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The diagram to the right shows the velocity-time graph for two masses $R$ and $S$ that collided elastically. Which of the following statements is true?
$(I)$ $R$ and $S$ moved in the same direction after the collision.
$(II)$ Kinetic energy of the system $(R$ & $S)$ is minimum at $t = 2$ milli sec.
$(III)$ The mass of $R$ was greater than mass of $S.$
The diagram to the right shows the velocity-time graph for two masses $R$ and $S$ that collided elastically. Which of the following statements is true?
$(I)$ $R$ and $S$ moved in the same direction after the collision.
$(II)$ Kinetic energy of the system $(R$ & $S)$ is minimum at $t = 2$ milli sec.
$(III)$ The mass of $R$ was greater than mass of $S.$
Answer the following :
$(a)$ The casing of a rocket in flight burns up due to friction. At whose expense is the heat energy required for burning obtained? The rocket or the atmosphere?
$(b)$ Comets move around the sun in highly elliptical orbits. The gravitational force on the comet due to the sun is not normal to the comet’s velocity in general. Yet the work done by the gravitational force over every complete orbit of the comet is zero. Why ?
$(c)$ An artificial satellite orbiting the earth in very thin atmosphere loses its energy gradually due to dissipation against atmospheric resistance, however small. Why then does its speed increase progressively as it comes closer and closer to the earth ?
$(d)$ In Figure $(i)$ the man walks $2\; m$ carrying a mass of $15\; kg$ on his hands. In Figure $(ii)$, he walks the same distance pulling the rope behind him. The rope goes over a pulley, and a mass of $15\; kg$ hangs at its other end. In which case is the work done greater ?
Answer the following :
$(a)$ The casing of a rocket in flight burns up due to friction. At whose expense is the heat energy required for burning obtained? The rocket or the atmosphere?
$(b)$ Comets move around the sun in highly elliptical orbits. The gravitational force on the comet due to the sun is not normal to the comet’s velocity in general. Yet the work done by the gravitational force over every complete orbit of the comet is zero. Why ?
$(c)$ An artificial satellite orbiting the earth in very thin atmosphere loses its energy gradually due to dissipation against atmospheric resistance, however small. Why then does its speed increase progressively as it comes closer and closer to the earth ?
$(d)$ In Figure $(i)$ the man walks $2\; m$ carrying a mass of $15\; kg$ on his hands. In Figure $(ii)$, he walks the same distance pulling the rope behind him. The rope goes over a pulley, and a mass of $15\; kg$ hangs at its other end. In which case is the work done greater ?