A particle is released from a height of S above the surface of the earth. At a certain height, its kinetic energy is three times its potential energy. The distance from the earth's surface and the speed of the particle at that instant are respectively:

1. $\frac{\mathrm{S}}{2},\frac{\sqrt{3\mathrm{gS}}}{2}$

2. $\frac{\mathrm{S}}{4},\sqrt{\frac{3\mathrm{gS}}{2}}$

3. $\frac{\mathrm{S}}{4},\frac{3\mathrm{gS}}{2}$

4. $\frac{\mathrm{S}}{4},\frac{\sqrt{3\mathrm{gS}}}{2}$

Subtopic: Conservation of Mechanical Energy |

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Body A of mass 4m moving with speed u collides with another body B of mass 2m at rest. The collision is head-on and elastic in nature. After the collision, the fraction of energy lost by the colliding body A is:

1. $\frac{5}{9}$

2. $\frac{1}{9}$

3. $\frac{8}{9}$

4. $\frac{4}{9}$

Subtopic: Collisions |

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When an object is shot from the bottom of a long, smooth inclined plane kept at an angle of 60$\xb0$ with horizontal, it can travel a distance ${x}_{1}$ along the plane. But when the inclination is decreased to 30$\xb0$ and the same object is shot with the same velocity, it can travel ${x}_{2}$ distance. Then ${x}_{1}$:${x}_{2}$ will be:

1. $1:2\sqrt{3}$

2. $1:\sqrt{2}$

3. $\sqrt{2}:1$

4. $1:\sqrt{3}$

Subtopic: Conservation of Mechanical Energy |

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A force F= 20+10y acts on a particle in the y-direction where F is in Newton and y is in meter. Work done by this force to move the particle from y = 0 to y = 1m is:

1. 20 J

2. 30 J

3. 5 J

4. 25 J

Subtopic: Work Done by Variable Force |

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A mass m is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when:

1. inclined at an angle of ${60}^{0}$ from vertical.

2. the mass is at the highest point.

3. the wire is horizontal.

4. the mass is at the lowest point.

Subtopic: Gravitational Potential Energy |

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A disc of radius 2 m and mass 100 kg rolls on a horizontal floor. Its centre of mass has speed of 20 cm/s. How much work is needed to stop it?

1. 1 J

2. 3 J

3. 30 J

4. 2 J

Subtopic: Work Energy Theorem |

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An object of mass 500 g initially at rest is acted upon by a variable force whose x-component varies with x in the manner shown. The velocities of the object at the points x = 8 m and x = 12 m would have the respective values of nearly:

1. 18 m/s and 24.4 m/s

2. 23 m/s and 24.4 m/s

3. 23 m/s and 20.5 m/s

4. 18 m/s and 20.5 m/s

Subtopic: Work Energy Theorem |

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Water falls from a height of 60m at the rate of 15kg/s to operate a turbine. The losses due to frictional forces are 10% of energy. How much power is generated by the turbine? (g=10 m/${s}^{2}$)

1. 8.1 kW 2. 10.2 kW

3. 12.3 kW 4. 7.0 kW

Subtopic: Power |

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The energy that will be ideally radiated by a 100 kW transmitter in 1 hour is :

1. 1 × 10^{5} J

2. 36 × 10^{7} J

3. 36 × 10^{4} J

4. 36 × 10^{5} J

1. 1 × 10

2. 36 × 10

3. 36 × 10

4. 36 × 10

Subtopic: Power |

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An electric lift with a maximum load of \(2000\) kg (lift+passengers) is moving up with a constant speed of \(1.5\) ms^{-1}. The frictional force opposing the motion is \(3000\) N. The minimum power delivered by the motor to the lift in watts is: (Take \(g=10\) ms^{-2})

1. \(23500\)

2. \(23000\)

3. \(20000\)

4. \(34500\)

1. \(23500\)

2. \(23000\)

3. \(20000\)

4. \(34500\)

Subtopic: Power |

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