Q. A horizontal force of 10 N is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is 0.2. The weight of the block is-
(1) 20 N
(2) 50 N
(3) 100 N
(4) 2 N

**[AIEEE – 2003]**
Q. A marble block of mass 2 kg lying on ice when given a velocity of 6 m/s is stopped by friction in 10s. Then the coefficient of friction is-
(1) 0.02 (2) 0.03 (3) 0.06 (4) 0.01

**[AIEEE – 2003]**
Q. A block rests on a rough inclined plane making an angle of $30^{\circ}$ with the horizontal. The coefficient of static friction between the block and the plane is 0.8. If the frictional force on the block is 10 N, the mass of the block (in kg) is : (taken $\left.\mathrm{g}=10 \mathrm{m} / \mathrm{s}^{2}\right)$
(1) 2.0 (2) 4.0 (3) 1.6 (4) 2.5

**[AIEEE – 2004]**
Q. A smooth block is released at rest on a $45^{\circ}$ incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is-
$(1) \mu_{\mathrm{k}}=1-\frac{1}{\mathrm{n}^{2}}$
$(2) \mu_{\mathrm{k}}=\sqrt{1-\frac{1}{\mathrm{n}^{2}}}$
(3) $\mu_{\mathrm{s}}=1-\frac{1}{\mathrm{n}^{2}}$
(4) $\mu_{\mathrm{s}}=\sqrt{1-\frac{1}{\mathrm{n}^{2}}}$

**[AIEEE – 2005]**
Q. The upper half of an inclined plane with inclination $\phi$ is perfectly smooth, while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom, if the coefficient of friction for the lower half is given by-
(1) $2 \sin \phi$
(2) $2 \cos \phi$
(3) 2 tan $\phi$
(4) $\tan \phi$

**[AIEEE – 2005]**
Q. Consider a car moving on a straight road with a speed of 100 m/s. The distance at which car can be stopped, is : $\left[\mu_{\mathrm{k}}=0.5\right]$
(1) 800 m (2) 1000 m (3) 100 m (4) 400 m

**[AIEEE – 2005]**
Q. The minimum force required to start pushing a body up a rough (frictional coefficient $\mu$) inclined plane is $\mathrm{F}_{1}$ while the minimum force needed to prevent it from sliding down is $\mathrm{F}_{2}$. If the inclined plane makes an angle $\theta$ from the horizontal such that $\tan \theta$ = $2 \mu$then the ratio $\frac{\mathrm{F}_{1}}{\mathrm{F}_{2}}$ is :-
(1) 4 (2) 1 (3) 2 (4) 3

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**Sol.**(4) $=\frac{2 \mu+\mu}{2 \mu-\mu}=\frac{3 \mu}{\mu}=3$

Q. A block of mass m is placed on a surface with a vertical cross section given by $\mathrm{y}=\frac{\mathrm{x}^{3}}{6}$ . If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is :-
(1) $\frac{1}{3} \mathrm{m}$
(2) $\frac{1}{2} \mathrm{m}$
(3) $\frac{1}{6} \mathrm{m}$
(4) $\frac{2}{3} \mathrm{m}$

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**Sol.**(3) For equilibrium under limiting friction $\operatorname{mg} \sin \theta=\mu \operatorname{mg} \cos \theta$ $\Rightarrow \tan \theta=\mu$ From the equation of surface $y=\frac{x^{3}}{6}$ slope $=\frac{d y}{d x}=\frac{3 x^{2}}{6}=\tan \theta$ $\Rightarrow \frac{\mathrm{x}^{2}}{2}=\mu=0.5 \Rightarrow \mathrm{x}=1$ So $\mathrm{y}=\frac{1}{6}$

Q. Given in the figure are two blocks A and B of weight 20 N and 100 N, respectively. These are being pressed against a wall by a force F as shown. If the coefficient of friction between the blocks is 0.1 and between block B and the wall is 0.15, the frictional force applied by the wall on block B is :-
(1) 120 N (2) 150 N (3) 100 N (4) 80 N

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**Sol.**(1) for equllibrrium of A $\mathrm{f}_{1}=20$ for equllibrrium of B $\mathrm{f}_{2}=\mathrm{f}_{1}+100$ $\mathrm{f}_{2}=120 \mathrm{N}$

Q. Two masses $\mathrm{m}_{1}$ = 5kg and $\mathrm{m}_{2}$ = 10kg, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is 0.15. The minimum weight m that should be put on top of $\mathrm{m}_{2}$ to stop the motion is :-
(1) 27.3 kg (2) 43.3 kg (3) 10.3 kg (4) 18.3 kg

**[JEE-(Mains) – 2018]**
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Option in last question is wrong, correct it.

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The answer of the last question is not matching with the options . Solution is right but it is not in the option . please correct it.

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