A motor cyclist moving with a velocity of $72\, km/hour$ on a flat road takes a turn on the road at a point where the radius of curvature of the road is $20$ meters. The acceleration due to gravity is $10 m/sec^2$. In order to avoid skidding, he must not bend with respect to the vertical plane by an angle greater than
$\theta = {\tan ^{ - 1}}6$
$\theta = {\tan ^{ - 1}}2$
$\theta = {\tan ^{ - 1}}25.92$
$\theta = {\tan ^{ - 1}}4$
A car of mass $1000\, kg$ negotiates a banked curve of radius $90\, m$ on a frictionless road. If the banking angle is $45^o $, the speed of the car is ....... $ms^{-1}$
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 ........ $N$
A vehicle of mass $200\,kg$ is moving along a levelled curved road of radius $70\,m$ with angular velocity of $0.2\,rad / s$. The centripetal force acting on the vehicle is $.........\,N$
A disc revolves with a speed of $33 \frac{1}{3}\; rev/min$, and has a radius of $15 \;cm .$ Two coins are placed at $4\; cm$ and $14 \;cm$ away from the centre of the record. If the co-efficient of friction between the coins and the record is $0.15,$ which of the coins will revolve with the record?
The maximum tension which an inextensible ring of mass $0.1\, kg/m$ can bear is $10\,N$. The maximum velocity in $m/s$ with which it can be rotated is ........ $m/s.$