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 $1.5 \ m$).
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A racing car travels on a track (without banking) $ABCDEPA$. $ABC$ is a circular arc of radius $2R$. $CD$ and $FA$ are straight paths of length $R$ and $DEF$ is a circular arc of radius $R = 100 \,m$. The coefficient of friction on the road is $\mu = 0.1$. The maximum speed of the car is $50\,ms^{-1}$. Find the minimum time for completing one round.
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 $T$ & $\omega .$
Four identical point masses $'m'$ joined by light string of length $'l'$ arrange such that they form square frame. Centre of table is coincide with centre of arrangment. If arrangement rotate with constant angular velocity $'\omega '$ , find out tension in each string
Defined a vehicle can be parked on a slope.
A $100 \,kg$ car is moving with a maximum velocity of $9 \,m/s$ across a circular track of radius $30\,m$. The maximum force of friction between the road and the car is ........ $N$