Imagine the situation in which the given arrangement is placed inside a trolley that can move only in the horizontal direction, as shown in figure. If the trolley is accelerated horizontally along the positive $x$ -axis with $a_0$, then Choose the correct statement $(s)$.
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A body of mass $4\, kg$ is at rest on a horizontal table. The coefficient of friction between the body and the table is $0.2$ . A horizontal force of $6N$ is applied on the body. The acceleration of the body is .......... $m/s^2$
A block of mass $10\, kg$ is placed on a rough horizontal surface having coefficient of friction $\,\mu = 0.5$. If a horizontal force of $100\, N$ is acting on it, then acceleration of the block will be ....... $m/s^2$
A railway line is taken round a circular arc of radius $1000\ m$, and is banked by raising the outer rail $h\ m$ above the inner rail. If the lateral force on the inner rail when a train travels round the curve at $10 \ ms^{-1}$ is equal to the lateral force on the outer rail when the train's speed is $20\ ms^{-1}$. The value of $4g\ tan\theta$ is equal to : (The distance between the rails is $1.5 \ m$).
A block of mass $10\, kg$ is placed on an inclined plane. When the angle of inclination is $30°$, the block just begins to slide down the plane. The force of static friction is ....... $kg\, wt$
A block of mass $m$ is on an inclined plane of angle $\theta$. The coefficient of friction between the block and the plane is $\mu$ and $\tan \theta>\mu$. The block is held stationary by applying a force $\mathrm{P}$ parallel to the plane. The direction of force pointing up the plane is taken to be positive. As $\mathrm{P}$ is varied from $\mathrm{P}_1=$ $m g(\sin \theta-\mu \cos \theta)$ to $P_2=m g(\sin \theta+\mu \cos \theta)$, the frictional force $f$ versus $P$ graph will look like
A body of mass $10$ kg slides along a rough horizontal surface. The coefficient of friction is $1/\sqrt 3 $. Taking $g = 10\,m/{s^2}$, the least force which acts at an angle of $30^o $ to the horizontal is ...... $N$
A coin is placed on a disc. The coefficient of friction between the coin and the disc is $\mu$. If the distance of the coin from the center of the disc is $r$, the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is: