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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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 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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A car of mass $$m$$ is moving on a level circular track of radius $$R$$. If $$\mu_s$$ represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by:
1. $$\sqrt{\frac{Rg}{\mu_s} }$$
2. $$\sqrt{\frac{mRg}{\mu_s}}$$
3. $$\sqrt{\mu_s Rg}$$
4. $$\sqrt{\mu_s m Rg}$$

Subtopic:  Friction |
87%
From NCERT
AIPMT - 2012
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A conveyor belt is moving at a constant speed of 2 m/s. A box is gently dropped on it. The coefficient of friction between them is µ = 0.5. The distance that the box will move relative to the belt before coming to rest on it, taking g = 10 ms–2 is:

 1 0.4 m 2 1.2 m 3 0.6 m 4 Zero
Subtopic:  Friction |
65%
From NCERT
AIPMT - 2011
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A block of mass $$\mathrm{m}$$ is in contact with the cart C as shown in the figure.

The coefficient of static friction between the block and the cart is $\mathrm{\mu }$. The acceleration $\mathrm{\alpha }$ of the cart that will prevent the block from falling satisfies:
1. $\mathrm{\alpha }>\frac{\mathrm{mg}}{\mathrm{\mu }}$

2. $\mathrm{\alpha }>\frac{\mathrm{g}}{\mathrm{\mu m}}$

3. $\mathrm{\alpha }\ge \frac{\mathrm{g}}{\mathrm{\mu }}$

4. $\mathrm{\alpha }<\frac{\mathrm{g}}{\mathrm{\mu }}$

Subtopic:  Friction |
81%
From NCERT
AIPMT - 2010
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A gramophone record is revolving with an angular velocity $\omega$. A coin is placed at a distance r from the centre of the record. The static coefficient of friction is $\mu$. The coin will revolve with the record if:

1. $r=\mu g{\omega }^{2}$

2. $r<\frac{{\omega }^{2}}{\mu g}$

3. $r\le \frac{\mu g}{{\omega }^{2}}$

4. $r\ge \frac{\mu g}{{\omega }^{2}}$

Subtopic:  Friction |
67%
From NCERT
AIPMT - 2010
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A block $$B$$ is pushed momentarily along a horizontal surface with an initial velocity $$v.$$ If $$\mu$$ is the coefficient of sliding friction between $$B$$ and the surface, the block $$B$$ will come to rest after a time:

1. $$v \over g \mu$$
2. $$g \mu \over v$$
3. $$g \over v$$
4. $$v \over g$$

Subtopic:  Friction |
79%
From NCERT
AIPMT - 2007
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