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Q. No.A mass of \(6~\text{kg}\) is suspended by a rope of negligible mass and a length of \(2~\text{m}\) from the ceiling. A force of \(60~\text{N}\) in the horizontal direction is applied at the mid-point \(P\) of the rope (see figure). The angle the rope makes with the vertical in equilibrium is:
(take \(g=10~\text{ms}^{-2}\))
1. \(15^\circ\)
2. \(30^\circ\)
3. \(45^\circ\)
4. \(60^\circ\)
(take \(g=10~\text{ms}^{-2}\))
1. \(15^\circ\)
2. \(30^\circ\)
3. \(45^\circ\)
4. \(60^\circ\)
Subtopic: Tension & Normal Reaction |
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If the tension in the cable supporting an elevator is equal to the weight of the elevator, the elevator may be:
| (a) | going up with increasing speed |
| (b) | going down with increasing speed |
| (c) | going up with uniform speed |
| (d) | going down with uniform speed |
Choose the correct option:
1. (a) and (b)
2. (b) and (c)
3. (c) and (d)
4. all of the above
Subtopic: Tension & Normal Reaction |
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A block of mass \(m\) slides down a smooth plane inclined at an angle of \(60^\circ\) with the horizontal. The normal reaction of the incline acting on the block equals:
| 1. | \(mg\sin60^\circ\) | 2. | \(mg\cos60^\circ\) |
| 3. | \(mg\tan60^\circ\) | 4. | \(mg\cot60^\circ\) |
Subtopic: Tension & Normal Reaction |
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The \(3~\text{kg},2~\text{kg}\) blocks lie on a smooth horizontal plane. The blocks are connected by a light, horizontal string which passes around a smooth, light pulley \(P\) (see figure). The pulley is pulled forward by a horizontal force of \(12~\text N.\) The accelerations of the blocks are \(a_1,a_2\) and that of the pulley is \(a_{\Large_P}.\) The tension in the string is \(T.\) The values of the quantities (in SI) are shown in column II, in a different order. Match the quantities with their correct values.
| Column I | Column II | ||
| \(\mathrm{(A)}\) | \(a_1\) | \(\mathrm{(I)}\) | \(2.5\) |
| \(\mathrm{(B)}\) | \(a_2\) | \(\mathrm{(II)}\) | \(2\) |
| \(\mathrm{(C)}\) | \(a_{\Large_P}\) | \(\mathrm{(III)}\) | \(6\) |
| \(\mathrm{(D)}\) | \(T\) | \(\mathrm{(IV)}\) | \(3\) |
| 1. | \(\mathrm{A\text-IV,B\text-III,C\text-II,D\text-I}\) |
| 2. | \(\mathrm{A\text-II,B\text-III,C\text-I,D\text-IV}\) |
| 3. | \(\mathrm{A\text-II,B\text-IV,C\text-I,D\text-III}\) |
| 4. | \(\mathrm{A\text-IV,B\text-II,C\text-III,D\text-I}\) |
Subtopic: Tension & Normal Reaction |
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In the system shown in the accompanying figure, what is the tension \(T_2?\)
| 1. | \(g\) | 2. | \(2g\) |
| 3. | \(5g\) | 4. | \(6g\) |
Subtopic: Tension & Normal Reaction |
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Two blocks \(A\) and \(B\) of masses \(3m\) and \(m\) respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in the figure. The magnitudes of acceleration of \(A\) and \(B\) immediately after the string is cut, are respectively:
1. \(\dfrac{g}{3},g\)
2. \(g,g\)
3. \(\dfrac{g}{3},\dfrac{g}{3}\)
4. \(g,\dfrac{g}{3}\)
Subtopic: Spring Force |
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A mass \(M\) is suspended by a light string from a rigid support. A force \(F\) is acting on the string as shown in the figure and the string makes an angle \(\theta\) with the vertical.
Which of the following expressions is correct?
Which of the following expressions is correct?
| 1. | \(T\mathrm{cos}\theta =F\) | 2. | \(T\mathrm{sin}\theta =Mg \) |
| 3. | \(F=Mg~\mathrm{tan}\theta \) | 4. | \(F=\mathrm{tan}\theta \) |
Subtopic: Tension & Normal Reaction |
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A cylinder of weight \( W\) rests on two smooth inclined planes forming a symmetric \(\mathrm{V} \text-\)groove, as shown in the figure. Which of the following correctly represents the free-body diagram of the cylinder?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Tension & Normal Reaction |
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The tension at the mid-point \(\mathrm{P}\) of the rope is:
(Consider the system is in equilibrium condition, mass of rope\(=4\) kg and \(g=10\) m/s2.)
1. \(100\) N
2. \(120\) N
3. \(140\) N
4. \(190\) N
(Consider the system is in equilibrium condition, mass of rope\(=4\) kg and \(g=10\) m/s2.)
1. \(100\) N
2. \(120\) N
3. \(140\) N
4. \(190\) N
Subtopic: Tension & Normal Reaction |
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A batsman hits back a ball of mass 0.4 kg straight in the direction of the bowler without changing its initial speed of 15 ms–1. The impulse imparted to the ball is:
1. 10 Ns
2. 11 Ns
3. 12 Ns
4. 13 Ns
1. 10 Ns
2. 11 Ns
3. 12 Ns
4. 13 Ns
Subtopic: Newton's Laws |
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