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The mass of a lift is 2000 kg. When the tension in the supporting cable is 28000 N, then its acceleration is: (g=10 m/s2)
1. 30 ms-2 downwards
2. 4 ms-2 upwards
3. 4 ms-2 downwards
4. 14 ms-2 upwards
Subtopic:  Types of Forces |
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Level 1: 80%+

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Four forces act on a body as shown in the figure: \(5~\text{N}\) to the right, \(6~\text{N}\) to the left, \(7~\text{N}\) upward and \(8~\text{N}\) downward. What additional force (magnitude and direction measured from the positive \(x\text-\)axis) must be applied so that the net acceleration of the body is zero?
1. \(\sqrt 2~ \text{N}, ~45^\circ\) 2. \(\sqrt 2~ \text{N},~ 135^\circ\)
3. \(\dfrac{2}{\sqrt 3}~ \text{N}, ~30^\circ\) 4. \(2~ \text{N}, ~45^\circ\)
Subtopic:  Types of Forces |
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Level 2: 60%+
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A person standing on a spring balance inside a stationary lift measures \(60\) kg. The weight of that person if the lift descends with the uniform downward acceleration of \(1.8\) m/s2 will be: [g \( = 10 \) m/s2 ]
1. \(321\) N
2. \(214\) N
3. \(163\) N
4. \(492\) N

Subtopic:  Tension & Normal Reaction |
 91%
Level 1: 80%+
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A uniform light wire of length \(2l\) is connected at its ends to two pegs \(A\) & \(B\) which are at the same (horizontal) level. The separation between the pegs is also \(2l,\) so that the wire is just stretched (without any tension). A weight \(W\) is suspended from the mid-point \((O)\) of the wire; and the mid-point is "depressed" below its initial level by \(y.\) Each 'half-wire', consequently, is inclined by a small angle \(\theta\) with the horizontal. The cross-section of the wire is \(\alpha.\)
                       
The tension in each 'half-wire' is, in terms of \(W,\theta,\):
1. \(\dfrac{W}{2\cos\theta}\)

2. \(\dfrac{W}{2\sin\theta}\)

3. \(\dfrac{W\sin\theta}{2}\)

4. \(\dfrac{W\cos\theta}{2}\)
Subtopic:  Tension & Normal Reaction |
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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. \(60^\circ\)
Subtopic:  Tension & Normal Reaction |
 85%
Level 1: 80%+
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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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Level 1: 80%+
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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:  Tension & Normal Reaction |
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Level 1: 80%+
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