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\(m_{1}\) moves on a slope making an angle \(\theta\) with the horizontal and is attached to mass \(m_{2}\) by a string passing over a frictionless pulley as shown in the figure. The coefficient of friction between \(m_{1}\) and the sloping surface is \(\mu\).

(a) | If \(m_{2} > m_{1} \text{sin} \theta \), the body will move up the plane. |

(b) | If \(m_{2} > m_{1} (\text{sin} \theta +\mu \text{cos} \theta)\), the body will move up the plane. |

(c) | If \(m_{2} < m_{1} (\text{sin} \theta +\mu \text{cos} \theta)\), the body will move up the plane. |

(d) | If \(m_{2} < m_{1} (\text{sin} \theta -\mu \text{cos} \theta)\), the body will move down the plane. |

Which of the following statement/s is/are true?

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

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

Subtopic: Friction |

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In figure a body \(A\) of mass \(m\) slides on a plane inclined at angle \(\left(\theta_{1}\right)\) to the horizontal and \(\mu\) is the coefficient of friction between \(A\) and the plane. \(A\) is connected by a light string passing over a frictionless pulley to another body \(B,\) also of mass \(m\), sliding on a frictionless plane inclined at an angle \(\left(\theta_{2}\right)\) to the horizontal.

(a) | A will never move up the plane |

(b) | A will just start moving up the plane when \(\mu = \frac{{\sin} \left(\theta\right)_{2} - {\sin} \left(\theta\right)_{1}}{{\cos} \left(\theta\right)_{1}}\) |

(c) | For \(A\) to move up the plane, \(\left(\theta\right)_{2}\) must always be greater than \(\left(\theta\right)_{1}\) |

(d) | \(B\) will always slide down with a constant speed |

Which of the following statement/s is/are true?

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

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

Subtopic: Friction |

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A body of mass \(10\) kg is acted upon by two perpendicular forces, \(6\) N and \(8\) N. The resultant acceleration of the body is:

(a) | \(1~\text{ms}^{-2}\) at an angle of \(\text {tan}^{-1} \left(\dfrac{4}{3}\right ) \) w.r.t. \(6\) N force |

(b) | \(0.2~\text{ms}^{-2}\) at an angle of \(\text {tan}^{-1} \left(\dfrac{3}{4}\right ) \) w.r.t. \(8\) N force |

(c) | \(1~\text{ms}^{-2}\) at an angle of \(\text {tan}^{-1} \left(\dfrac{3}{4}\right ) \) w.r.t. \(8\) N force |

(d) | \(0.2~\text{ms}^{-2}\) at an angle of \(\text {tan}^{-1} \left(\dfrac{3}{4}\right ) \) w.r.t. \(6\) N force |

Choose the correct option:

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

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

Subtopic: Application of Laws |

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In the figure, the coefficient of friction between the floor and body \(B\) is \(0.1.\) The coefficient of friction between bodies \(B\) and \(A\) is \(0.2.\) A force \(F\) is applied as shown on \(B.\) The mass of \(A\) is \(rn/2\) and of \(B\) is \(m.\)

(a) | The bodies will move together if \(F = 0.25\text{mg}\) |

(b) | The \(A\) will slip with \(B\) if \(F = 0.5\text{mg}\) |

(c) | The bodies will move together if \(F = 0.5\text{mg}\) |

(d) | The bodies will be at rest if \(F = 0.1\text{mg}\) |

(e) | The maximum value of \(F\) for which the two bodies will move together is \(0.45\text{mg}\) |

Which of the following statement(s) is/are true?

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

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

Subtopic: Application of Laws | Friction |

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The motion of a particle of mass \(m\) is given by \(x=0\) for \(t<0 ~\text s\), \(x(t)=A~\text {sin}~4\pi t\) for \(0<t<(1/4) \text s ~(A>0)\), and \(x=0\) for \(t>(1/4) ~\text s\). Then:

(a) | The force at \(t=(1/8) ~\text s \) on the particle is \(-16 \pi^2\text{Am}\) |

(b) | The particle is acted upon by an impulse of magnitude \(4 \pi^2 \text{Am}\) at \(t=0 ~\text s\) and \(t=(1/4) ~\text s\) |

(c) | The particle is not acted upon by any force |

(d) | The particle is not acted upon by a constant force |

(e) | There is no impulse acting on the particle |

Which of the following statement/s is/are true?

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

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

Subtopic: Newton's Laws | Application of Laws |

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A car of mass \(m\) starts from rest and acquires a velocity along the east, \(v=v\mathrm{\hat{i}}(v>0)\) in two seconds. Assuming the car moves with uniform acceleration, the force exerted on the car is:

1. | \(mv/2 \) eastward and is exerted by the car engine. |

2. | \(mv/2\) eastward and is due to the friction on the tires exerted by the road. |

3. | more than \(mv/2\) eastward exerted due to the engine and overcomes the friction of the road. |

4. | \(mv/2\) exerted by the engine. |

Subtopic: Newton's Laws | Application of Laws |

54%

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A body with a mass of \(5\) kg is acted upon by a force \(\vec{F}=\left ( -3\hat{i} +4\hat{j}\right )\) N. If its initial velocity at \(t=0\) is \(\vec{v}=\left ( 6\hat{i} -12\hat{j}\right )\) m/s, the time at which it will just have a velocity along the Y-axis is:

1. never

2. \(10\) s

3. \(2\) s

4. \(15\) s

Subtopic: Newton's Laws |

56%

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A body of mass \(2~\text{kg}\) travels according to the law \(x \left( t \right) = pt + qt^2+ rt^3\) where,\(\) \(p = 3 ~\text{ms }^{−1 },\) \(q = 4 ~\text{ms }^{−2}\) and \(r = 5 ~\text{ms }^{−3}\). The force acting on the body at \(t = 2 ~\text{s }\) is

1. | \(136~\text{N}\) | 2. | \(134~\text{N}\) |

3. | \(158~\text{N}\) | 4. | \(68~\text{N}\) |

Subtopic: Newton's Laws | Application of Laws |

66%

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A hockey player is moving northward and suddenly turns westward at the same speed to avoid an opponent. The force that acts on the player is:

1. | frictional force along westward |

2. | muscle force along southward |

3. | frictional force along south-West |

4. | muscle force a south-West |

Subtopic: Newton's Laws | Application of Laws |

67%

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Conservation of momentum in a collision between particles can be understood from:

1. | conservation of energy |

2. | newton's first law only |

3. | newton's second law only |

4. | both Newton's second and third law |

Subtopic: Newton's Laws | Application of Laws |

51%

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