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 \(10~\text{m}\) with a constant speed of \(10~\text{m/s}\). A plumb bob is suspended from the roof of the car by a light rigid rod of length \(1.00~\text{m}\). 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 

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

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

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

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

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