The normal reaction $'{N}^{\prime}$ for a vehicle of $800\, {kg}$ mass, negotiating a turn on a $30^{\circ}$ banked road at maximum possible speed without skidding is $...\,\times 10^{3}\, {kg} {m} / {s}^{2}$ [Given $\left.\cos 30^{\circ}=0.87, \mu_{{s}}=0.2\right]$

A body of mass $m$ is tied to one end of a spring and whirled round in a horizontal plane with a constant angular velocity. The elongation in the spring is one centimetre. If the angular velocity is doubled, the elongation in the spring is $5\, cm$ . The original length of the spring is ............ $cm$

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?

For a body moving in a circular path, a condition for no skidding if $\mu $ is the coefficient of friction, is

A mass is supported on a frictionless horizontal surface. It is attached to a string and rotates about a fixed centre at an angular velocity ${\omega _0}$. If the length of the string and angular velocity are doubled, the tension in the string which was initially ${T_0}$ is now

An aircraft executes a horizontal loop at a speed of $720\; km/h$ with its wings banked at $15^o$. What is the radius of the loop in $km$?