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 |
 80%
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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A balloon with mass \(m\) is descending down with an acceleration \(a\) (where \(a<g\)). How much mass should be removed from it so that it starts moving up with an acceleration \(a\)?

1. \( \frac{2 m a}{g+a} \) 2. \( \frac{2 m a}{g-a} \)
3. \( \frac{m a}{g+a} \) 4. \( \frac{m a}{g-a}\)

Subtopic:  Application of Laws |
 62%
From NCERT
AIPMT - 2014
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The upper half of an inclined plane of inclination \(\theta\) is perfectly smooth while the lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom if the coefficient of friction between the block and the lower half of the plane is given by:
1. \(\mu=2/tan \theta\)
2. \(\mu=2tan \theta\)
3. \(\mu=tan \theta\)
4. \(\mu=1/tan \theta\)

Subtopic:  Friction |
 65%
From NCERT
AIPMT - 2013
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Three blocks with masses \(m\), \(2m\), and \(3m\) are connected by strings as shown in the figure. After an upward force \(F\) is applied on block \(m\), the masses move upward at constant speed \(v\). What is the net force on the block of mass \(2m\)? (\(g\) is the acceleration due to gravity)

           
1. \(2~mg\)
2. \(3~mg\)
3. \(6~mg\)
4. zero
Subtopic:  Application of Laws |
 75%
From NCERT
AIPMT - 2013
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A car is moving in a circular horizontal track of radius \(10\) m with a constant speed of \(10\) m/s. A bob is suspended from the roof of the car by a light wire of length \(1.0\) m. The angle made by the wire with the vertical is: 
1. \(\pi \over 3 \)
2. \(\pi \over 6\)
3. \(\pi \over 4\)
4. \(0^\circ\)
Subtopic:  Uniform Circular Motion |
 71%
From NCERT
NEET - 2013
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