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)
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A force of $750 \,N$ is applied to a block of mass $102\, kg$ to prevent it from sliding on a plane with an inclination angle $30°$ with the horizontal. If the coefficients of static friction and kinetic friction between the block and the plane are $0.4 $ and $0.3$ respectively, then the frictional force acting on the block is...... $N$
If the radius of curvature of the path of two particles of same mass are in the ratio $3:4,$ then in order to have constant centripetal force, their velocities will be in the ratio of:
A train is running at $20 \,m / s$ on a railway line with radius of curvature $40,000$ metres. The distance between the two rails is $1.5$ metres. For safe running of train the elevation of outer rail over the inner rail is ......$mm$ $\left( g =10 \,m / s ^2\right)$
A system of two blocks of masses $m =2 \; kg$ and $M=8 \; kg$ is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is $0.5$. The maximum horizontal force $F$ that can be applied to the block of mass $M$ so that the blocks move together will be $\dots \; N$
The upper half of an inclined plane of inclination $\theta$ is perfectly smooth while the lower half is rough. A body starting from the rest at top comes back to rest at the bottom if the coefficient of friction for the lower half is given by
The time taken by an object to slide down $45^{\circ}$ rough inclined plane is $n$ times as it takes to slide down a perfectly smooth $45^{\circ}$ incline plane. The coefficient of kinetic friction between the object and the incline plane is
If a cyclist moving with a speed of $4.9\, m/s$ on a level road can take a sharp circular turn of radius $4 \,m$, then coefficient of friction between the cycle tyres and road is
An annular ring with inner and outer radii $R_{1}$ and $R_{2}$ is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, $\frac{F_{1}}{F_{2}}$ is