Normal Reaction

Q. A block of mass of $10kg$ is in contact with the inner wall of a hollow cylindrical drum of radius $1m.$ The coefficient of friction between the block and the inner wall of the cylinder is $0.1.$ The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be $\left(g=10m/s^2\right)$

1. $\sqrt{10}\frac{rad}{s}$
2. $\frac{10}{2\pi }\frac{rad}{s}$
3. $10\frac{rad}{s}$
4. $10\pi \frac{rad}{s}$

Q. The normal reaction between the blocks $N_1,N_2$ are

1. $50N,20N$
2. $100N,50N$
3. $50N,200N$
4. $100N,20N$

Q. Two blocks $m_1$ and $m_2$ are resting on a rough inclined plane of inclination ${37}^{\circ }$ as shown in figure. The contact force between the blocks is, $(m_1=4\text{kg},m_2=2\text{kg},{\mu }_1=0.8,{\mu }_2=0.5,g=10{\text{m/s}}^2,\sin {37}^{\circ }=3/5)$

1. $3.2\text{N}$
2. $3.6\text{N}$
3. $7.2\text{N}$
4. Zero

Q. A body is moving down along an inclined plane of slope ${37}^{\circ }$. The co-efficient of friction between the body and plane varies as $\mu =0.3x$, where $x$ is distance travelled down the plane. The body will have maximum speed at $x$ equal to
$[\sin {37}^{\circ }=3/5\text{and}g=10{\text{m/s}}^2]$

1. $2.5\text{m}$
2. $2.26\text{m}$
3. $1.16\text{m}$
4. $2\text{m}$

Q. An insect crawls up a hemispherical surface very slowly as shown in the figure. The coefficient of static friction between the insect and the surface is $\frac{1}{3}$. If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical, then the maximum possible value of $\alpha$ is given by

1. $\cot \alpha =3$
2. $\tan \alpha =3$
3. $\sec \alpha =3$
4. $\cos \alpha =3$