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. $$\sqrt{\mathrm{gR}^2\left(\frac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\mathrm{s}} \tan \theta}\right)}$$

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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