A block of mass $m$ is kept on horizontal turn table at $x$ distance from the centre. If coefficient of friction between block and surface of turn table is $\mu$, then maximum angular speed of the table so that block does not slip
$\sqrt{\frac{\mu g}{x^2}}$
$\sqrt{\frac{\mu g}{x}}$
$\sqrt{\frac{\mu g}{2 x}}$
$\sqrt{\frac{\mu x^2}{g}}$
$A$ particle inside the rough surface of $a$ rotating cone about its axis is at rest relative to it at $a$ height of $1m$ above its vertex. Friction coefficient is $\mu = 0.5$, if half angle of cone is $45^o$, the maximum angular velocity of revolution of cone can be :
For a vehicle moving on a banked curved road, using free body diagram $(FBD)$, obtain the formula for the maximum safe speed $(v_{max})$.
The maximum speed that can be achieved without skidding by a car on a circular unbanked road of radius $R$ and coefficient of static friction $\mu $, is
In a conical pendulum, the bob is rotated with different angular velocities and tension in the string is calculated for different values of $\omega$ . Which of them is correct graph between $T$ & $\omega .$
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 $1.5 \ m$).