A car of mass $800 \,kg$ moves on a circular track of radius $40\, m$. If the coefficient of friction is $0.5$, then maximum velocity with which the car can move is ......... $m/s$
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Two masses $m_1 = 5\ kg$ and $m_2 = 10\ kg$, 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 $m_2$ to stop the motion is ........ $kg$
In the arrangement shown in the figure, mass of the block $B$ and $A$ is $2m$ and $m$ respectively. Surface between $B$ and floor is smooth. The block $B$ is connected to the block $C$ by means of a string pulley system. If the whole system is released, then find the minimum value of mass of block $C$ so that block $A$ remains stationary $w.r.t. B$. Coefficient of friction between $A$ and $B$ is $\mu$
A cube of mass $m$ slides down an inclined right-angle trough. If the coefficient of kinetic friction between the cube and the trough is $\mu _k$ , then the acceleration of the block is
A horizontal force of $4\,N$ is needed to keep a block of mass $0.5\, kg$ sliding on a horizontal surface with a constant speed. The coefficient of sliding friction must be :- $[g = 10\, m/s^2]$
A rope of length $L$ and mass $M$ is being pulled on a rough horizontal floor by a constant horizontal force $F$ = $Mg$ . The force is acting at one end of the rope in the same direction as the length of the rope. The coefficient of kinetic friction between rope and floor is $1/2$ . Then, the tension at the midpoint of the rope is
A motor car has a width $1.1$ m between wheels. Its centre of gravity is $0.62$ m above the ground and the coefficient of friction between the wheels and the road is $0.8$. ...... $m/s$ is the maximum possible speed, if the centre of gravity inscribes a circle of radius $15$ m ? (Road surface is horizontal)
The blocks $A$ and $B$ are arranged as shown in the figure. The pulley is frictionless. The mass of $A$ is $10 \,kg$. The coefficient of friction of $A$ with the horizontal surface is $0.20$. The minimum mass of $B $ to start the motion will be...... $kg$
The coefficient of friction between $4kg$ and $5\, kg$ blocks is $0.2$ and between $5kg$ block and ground is $0.1$ respectively. Choose the correct statements
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 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 ........ $N$