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A stone tied to the end of a \(1\) m long string is whirled in a horizontal circle at a constant speed. If the stone makes \(22\) revolutions in \(44\) seconds, what is the magnitude and direction of acceleration of the stone?

1. | \(\pi^2 ~\text{ms}^{-2} \) and direction along the tangent to the circle. |

2. | \(\pi^2 ~\text{ms}^{-2} \) and direction along the radius towards the centre. |

3. | \(\frac{\pi^2}{4}~\text{ms}^{-2} \) and direction along the radius towards the centre. |

4. | \(\pi^2~\text{ms}^{-2} \) and direction along the radius away from the centre. |

Subtopic: Circular Motion |

77%

From NCERT

AIPMT - 2005

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Two boys are standing at the ends \(A\) and \(B\) of the ground where \(AB =a.\) The boy at \(B\) starts running in a direction perpendicular to \(AB\) with velocity \(v_1.\) The boy at \(A\) starts running simultaneously with velocity \(v\) and catches the other boy in a time \(t,\) where \(t\) is:

1. | \(\frac{a}{\sqrt{v^2+v^2_1}}\) | 2. | \(\frac{a}{\sqrt{v^2-v^2_1}}\) |

3. | \(\frac{a}{v-v_1}\) | 4. | \(\frac{a}{v+v_1}\) |

Subtopic: Relative Motion |

62%

From NCERT

AIPMT - 2005

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Two particles are separated by a horizontal distance \(x\) as shown in the figure. They are projected at the same time as shown in the figure with different initial speeds. The time after which the horizontal distance between them becomes zero will be:

1. | \(\frac{x}{u}\) | 2. | \(\frac{u}{2 x}\) |

3. | \(\frac{2 u}{x}\) | 4. | None of the above |

Subtopic: Relative Motion |

66%

From NCERT

AIPMT - 1999

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Two particles are projected with the same initial velocity, one makes an angle \(\theta\) with the horizontal while the other makes an angle \(\theta\) with the vertical. If their common range is \(R\), then the product of their time of flight is directly proportional to:

1. \(R\)

2. \(R^2\)${\mathrm{}}^{}$

3. \(\frac{1}{R}\)

4. \(R^{0}\)

Subtopic: Projectile Motion |

66%

From NCERT

AIPMT - 1999

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A particle \((A)\) is dropped from a height and another particle \((B)\) is projected in a horizontal direction with a speed of \(5\) m/s from the same height. The correct statement, from the following, is:

1. | Particle \((A)\) will reach the ground first with respect to particle \((B)\). |

2. | Particle \((B)\) will reach the ground first with respect to particle \((A)\). |

3. | Both particles will reach the ground at the same time. |

4. | Both particles will reach the ground at the same speed. |

Subtopic: Projectile Motion |

78%

From NCERT

AIPMT - 2002

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A particle moves along a circle of radius \(\frac{20}{\pi}~\text{m}\) with constant tangential acceleration. If the velocity of the particle is \(80\) m/s at the end of the second revolution after motion has begun, the tangential acceleration is:

1. \(40\) ms^{–2 }

2. \(640\pi\) ms^{–2 }

3. \(160\pi\) ms^{–2 }

4. \(40\pi\) ms^{–2 }

Subtopic: Circular Motion |

57%

From NCERT

AIPMT - 2003

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The position of a particle is given by;

\(\vec{r}=(3.0t\hat{i}-2.0t^{2}\hat{j}+4.0\hat{k})\) m where \(t\) is in seconds and the coefficients have the proper units for \(r\) to be in metres. The magnitude and direction of \(\vec{v}(t)\) at\(t=1.0\) s are:

1. \(4\)m/s,\(53^\circ\) with \(x\)-axis

2. \(4\) m/s, \(37^\circ\) with \(x\)-axis

3. \(5\) m/s,\(53^\circ\) with \(y\)-axis

4. \(5\)m/s, \(53^\circ\) with \(x\)-axis

\(\vec{r}=(3.0t\hat{i}-2.0t^{2}\hat{j}+4.0\hat{k})\) m where \(t\) is in seconds and the coefficients have the proper units for \(r\) to be in metres. The magnitude and direction of \(\vec{v}(t)\) at\(t=1.0\) s are:

1. \(4\)m/s,\(53^\circ\) with \(x\)-axis

2. \(4\) m/s, \(37^\circ\) with \(x\)-axis

3. \(5\) m/s,\(53^\circ\) with \(y\)-axis

4. \(5\)m/s, \(53^\circ\) with \(x\)-axis

Subtopic: Speed & Velocity |

68%

From NCERT

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A particle starts from the origin at \(t=0\) with a velocity of \(5.0\hat i\) m/s and moves in the \(x\text-y\) plane under the action of a force that produces a constant acceleration of \((3.0\hat i + 2.0 \hat j)~\text{m/s}^2\)${\mathrm{}}^{}$. What is the y-coordinate of the particle at the instant its \(x\text-\)coordinate is \(84\) m?

1. \(36\) m

2. \(26\) m

3. \(1\) m

4. \(0\) m

Subtopic: Uniformly Accelerated Motion |

63%

From NCERT

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A particle starts from the origin at \(t=0\) with a velocity of \(5.0\hat i\) m/s and moves in the \(x\text-y\) plane under the action of a force that produces a constant acceleration of \((3.0\hat i + 2.0\hat j)~\text{m/s}^2\). What is the speed of the particle at the instant its \(x\text-\)coordinate is \(84\) m?

1. | \(36\) m/s | 2. | \(26\) m/s |

3. | \(1\) m/s | 4. | \(0\) m/s |

Subtopic: Uniformly Accelerated Motion |

70%

From NCERT

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If two projectiles, with the same masses and with the same velocities, are thrown at an angle \(60^\circ\) & \(30^\circ\) with the horizontal, then which of the following quantities will remain the same?

1. | time of flight |

2. | horizontal range of projectile |

3. | maximum height acquired |

4. | all of the above |

Subtopic: Projectile Motion |

79%

From NCERT

AIPMT - 2000

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