A massless and inextensible string connects two blocks \(\mathrm{A}\) and \(\mathrm{B}\) of masses \(3m\) and \(m,\) respectively. The whole system is suspended by a massless spring, as shown in the figure. The magnitudes of acceleration of \(\mathrm{A}\) and \(\mathrm{B}\) immediately after the string is cut, are respectively:
         

1. \(\frac{g}{3},g\) 2. \(g,g\)
3. \(\frac{g}{3},\frac{g}{3}\) 4. \(g,\frac{g}{3}\)

Subtopic:  Spring Force |
 69%
From NCERT
NEET - 2017
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One end of the string of length \(l\) is connected to a particle of mass \(m\) and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in a circle with speed \(v\), the net force on the particle (directed towards the center) will be: (\(T\) represents the tension in the string)
1. \(T+\frac{m v^2}{l}\)
2. \(T-\frac{m v^2}{l}\)
3. zero
4. \(T\)

Subtopic:  Non Uniform Vertical Circular Motion |
 51%
From NCERT
NEET - 2017
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A block of mass \(m\) is placed on a smooth inclined wedge \(ABC\) of inclination \(\theta\) as shown in the figure. The wedge is given an acceleration '\(a\)' towards the right. The relation between \(a\) and \(\theta\) for the block to remain stationary on the wedge is:
          
1. \(a = \frac{g}{\text{cosec}\theta}\)
2. \(a = \frac{g}{\text{sin}\theta}\)
3. \(a = g~\text{cos}\theta\)
4. \(a = g~\text{tan}\theta\)

Subtopic:  Application of Laws |
 78%
From NCERT
NEET - 2018
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A car is negotiating a curved road of radius \(R\). The road is banked at an angle \(\theta\). The coefficient of friction between the tyre of the car and the road is \(\mu_s\). The maximum safe velocity on this road is:
1. \(\sqrt{\operatorname{gR}\left(\frac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\mathrm{s}} \tan \theta}\right)}\)
2. \(\sqrt{\frac{\mathrm{g}}{\mathrm{R}}\left(\frac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\mathrm{s}} \tan \theta}\right)}\)
3. \(\sqrt{\frac{\mathrm{g}}{\mathrm{R}^2}\left(\frac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\operatorname{s}} \tan \theta}\right)}\)
4. \(\sqrt{\mathrm{gR}^2\left(\frac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\mathrm{s}} \tan \theta}\right)}\)

Subtopic:  Banking of Roads |
 88%
From NCERT
NEET - 2016
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A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches \(30^\circ\), the box starts to slip and slides \(4.0\) m down the plank in \(4.0\) s. The coefficients of static and kinetic friction between the box and the plank will be, respectively:
              

1. \(0.6\) and \(0.6\) 
2. \(0.6\) and \(0.5\) 
3. \(0.5\) and \(0.6\) 
4. \(0.4\) and \(0.3\)
Subtopic:  Friction |
 70%
From NCERT
NEET - 2015
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Two stones of masses \(m\) and \(2m\) are whirled in horizontal circles, the heavier one in a radius \(\frac{r}{2}\) and the lighter one in a radius \(r\). The tangential speed of lighter stone is \(n\) times that of the value of heavier stone when they experience the same centripetal forces. The value of \(n\) is:

1. \(3\) 2. \(4\)
3. \(1\) 4. \(2\)
Subtopic:  Uniform Circular Motion |
From NCERT
NEET - 2015
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Three blocks \(\mathrm{A}\), \(\mathrm{B}\), and \(\mathrm{C}\) of masses \(4~\text{kg}\), \(2~\text{kg}\), and \(1~\text{kg}\) respectively, are in contact on a frictionless surface, as shown. If a force of \(14~\text{N}\) is applied to the \(4~\text{kg}\) block, then the contact force between \(\mathrm{A}\) and \(\mathrm{B}\) is: 
          
1. \(2~\text{N}\)
2. \(6~\text{N}\)
3. \(8~\text{N}\)
4. \(18~\text{N}\)

Subtopic:  Tension & Normal Reaction |
 81%
From NCERT
NEET - 2015
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A block \(\mathrm{A}\) of mass \(m_1\) rests on a horizontal table. A light string connected to it passes over a frictionless pulley at the edge of the table and from its other end, another block \(\mathrm{B}\) of mass \(m_2\) is suspended. The coefficient of kinetic friction between block \(\mathrm{A}\) and the table is \(\mu_k\). When block \(\mathrm{A}\) is sliding on the table, the tension in the string is:
1. \( \frac{\left({m}_2+\mu_{{k}}{m}_1\right) {g}}{\left({m}_1+{m}_2\right)}\)
2. \( \frac{\left({m}_2-\mu_{{k}} {m}_1\right) {g}}{\left({m}_1+{m}_2\right)}\)
3. \(\frac{{m}_1 {~m}_2\left(1-\mu_{{k}}\right) {g}}{\left({m}_1+{m}_2\right)}\)
4. \( \frac{{m}_1 {~m}_2\left(1+\mu_{{k}}\right)}{{m}_1+{m}_2} \mathrm{~g}\)

Subtopic:  Friction |
 53%
From NCERT
NEET - 2015
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A system consists of three masses \(m_1\), \(m_2\), and \(m_3\) connected by a string passing over a pulley \(\mathrm{P}\). The mass \(m_1\) hangs freely, and \(m_2\) and \(m_3\) are on a rough horizontal table (the coefficient of friction = \(\mu\)). The pulley is frictionless and of negligible mass. The downward acceleration of mass \(m_1\) is: (Assume \(m_1=m_2=m_3=m\) and \(g\) is the acceleration due to gravity.) 
             
1. \(\frac{g(1-g \mu)}{9}\)
2. \(\frac{2 g \mu}{3}\)
3. \( \frac{g(1-2 \mu)}{3}\)
4. \(\frac{g(1-2 \mu)}{2}\)

Subtopic:  Friction |
 84%
From NCERT
AIPMT - 2014
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The force \(\mathrm{F}\) acting on a particle of mass \(\mathrm{m}\) is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from \(0\) to \(8\) s is:
        

1. \(24\) N-s 2. \(20\) N-s
3. \(12\) N-s 4. \(6\) N-s
Subtopic:  Newton's Laws |
 83%
From NCERT
AIPMT - 2014
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