A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/sec. A plumb bob is suspended from the roof of the car by a light rigid rod of length 1.00 m. The angle made by the rod with the track is

1.  Zero

2.  30$°$

3.  45$°$

4.  60$°$

A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/sec. A plumb bob is suspended from the roof of the car by a light rigid rod of length 1.00 m. The angle formed by the rod with respect to the vertical is:

A car is negociating a curved road of radius R. The road is banked at angle $\mathrm{\theta }$. The coefficient of friction between the car and the road is ${\mu }_s$. The maximum safe velocity on this road is 

(a)$\sqrt{gR\left(\frac{\tan \theta +\mu s}{1-{\mu }_s\tan \theta }\right)}$ 

(b) $\sqrt{\frac{g}{R}\left(\frac{\tan \theta +\mu s}{1-{\mu }_s\tan \theta }\right)}$

(c) $\sqrt{\frac{g}{R^2}\left(\frac{\tan \theta +\mu s}{1-{\mu }_s\tan \theta }\right)}$

(d) $\sqrt{g{R}^2\left(\frac{\tan \theta +\mu s}{1-{\mu }_s\tan \theta }\right)}$

The slope of a smooth banked horizontal surface road is $p$. If the radius of the curve be $r$, the maximum velocity with which a car can negotiate the curve is given by

(a) $prg$

(b) $\sqrt{prg}$

(c) $p\mathit{/}rg$

(d) $\sqrt{p\mathit{/}rg}$

The angle of banking at the turning of a road does not depend upon the

(a) Mass of vehicle

(b) Acceleration due to gravity

(c) The velocity of the vehicle

(d) Radius of the curved path

Traffic is moving at 60 km/hr along a circular track of radius 0.2 km, the correct angle of banking is

1.  ${\tan }^{-1}\left(\frac{60}{9.8\times 0.2}\right)$

2.  ${\tan }^{-1}\left(\frac{60\times 9.8}{200}\right)$

3.  ${\tan }^{-1}\left(\frac{{\left({\displaystyle \frac{50}{3}}\right)}^2}{200\times 9.8}\right)$

4.  ${\tan }^{-1}\left(\frac{{\displaystyle \frac{50}{3}}}{200\times 9.8}\right)$

A car is negotiating a curved road of radius \(R\). The road is banked at an angle \(\theta\). The coefficient of friction between the tyre of the car and the road is \(\mu_s\). The maximum safe velocity on this road is:
1. \(\sqrt{\operatorname{gR}\left(\frac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\mathrm{s}} \tan \theta}\right)}\)
2. \(\sqrt{\frac{\mathrm{g}}{\mathrm{R}}\left(\frac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\mathrm{s}} \tan \theta}\right)}\)
3. \(\sqrt{\frac{\mathrm{g}}{\mathrm{R}^2}\left(\frac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\operatorname{s}} \tan \theta}\right)}\)
4. \(\sqrt{\mathrm{gR}^2\left(\frac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\mathrm{s}} \tan \theta}\right)}\)

A car of mass \(1000\) kg negotiates a banked curve of radius \(90\) m on a frictionless road. If the banking angle is of \(45^\circ,\) the speed of the car is:

An aircraft executes a horizontal loop at a speed of \(720\) km/h with its wings banked at \(15^{\circ}\). What is the radius of the loop? (Take \(g=10~\text{m/s}^{2}\), \(\tan 15^{\circ}=0.27\))$$
1. \(1.30\) km
2. \(14.9\) km
3. \(1.55\) km
4. \(20.9\) km