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In a two-dimensional motion, instantaneous speed \(v_0\) is a positive constant. Then which of the following is necessarily true?

1. | The acceleration of the particle is zero. |

2. | The acceleration of the particle is increasing. |

3. | The acceleration of the particle is necessarily in the plane of motion. |

4. | The particle must be undergoing a uniform circular motion. |

Subtopic: Â Acceleration |

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A particle slides down a frictionless parabolic track starting from rest at point \(A\). Point \(B\) is at the vertex of the parabola and point \(C\) is at a height less than that of point \(A\). After \(C\), the particle moves freely in the air as a projectile. If the particle reaches the highest point at \(P\), then,

** **

1. | kinetic energy at \(P\) = kinetic energy at \(B\) |

2. | height at \(P\) = height at \(A\) |

3. | total energy at \(P\) = total energy at \(A\) |

4. | time of travel from \(A\) to \(B\) = time of travel from \(B\) to \(P\) |

Subtopic: Â Uniformly Accelerated Motion |

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The following are four different relations about displacement, velocity and acceleration for the motion of a particle in general.

(a) | \(v_{a v}=1 / 2\left[v\left(t_1\right)+v\left(t_2\right)\right]\) |

(b) | \(v_{{av}}={r}\left({t}_2\right)-{r}\left({t}_1\right) / {t}_2-{t}_1\) |

(c) | \(r=1 / 2\left[v\left(t_2\right)-v\left(t_1\right)\right]\left({t}_2-{t}_1\right)\) |

(d) | \({a}_{{av}}=v\left({t}_2\right)-v\left({t}_1\right) / {t}_2-{t}_1\) |

The incorrect alternative/s is/are:

1. | (a), (d) | 2. | (a), (c) |

3. | (b), (c) | 4. | (a), (b) |

Subtopic: Â Speed & Velocity |

Â 58%

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For a particle performing uniform circular motion,

(a) | the magnitude of particle velocity (speed) remains constant. |

(b) | particle velocity is always perpendicular to the radius vector. |

(c) | the direction of acceleration keeps changing as the particle moves. |

(d) | angular momentum is constant in magnitude but direction keeps changing. |

Choose the correct statement/s:

1. | (c), (d) | 2. | (a), (c) |

3. | (b), (c) | 4. | (a), (b), (c) |

Subtopic: Â Circular Motion |

Â 74%

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Two particles are projected in the air with speed \(v_0\), at angles \(\theta_1\) and \(\theta_2\) to the horizontal, respectively. If the height reached by the first particle is greater than that of the second, then:

(a) | the angle of the projection: \(\theta_1>\theta_2\) |

(b) | the time of flight: \(T_1>T_2\) |

(c) | the horizontal range: \(R_1>R_2\) |

(d) | the total energy: \(U_1>U_2\) |

Choose the correct option:

1. (a), (c), (d)

2. (a), (c)

3. (b), (c), (d)

4. (a), (b)

Subtopic: Â Projectile Motion |

Â 67%

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In a two-dimensional motion, instantaneous speed \(v_0\) is a positive constant. Then which of the following is necessarily true?

1. | the average velocity is not zero at any time. |

2. | average acceleration must always vanish. |

3. | displacements in equal time intervals are equal. |

4. | equal path lengths are traversed in equal intervals. |

Subtopic: Â Speed & Velocity |

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The horizontal range of a projectile fired at an angle of \(15^\circ\) is \(50\) m. If it is fired with the same speed at an angle of \(45^\circ\), its range will be:

1. \(60\) m

2. \(71\) m

3. \(100\) m

4. \(141\) m

Subtopic: Â Projectile Motion |

Â 82%

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