Question

A boy on a cycle pedals around a circle of 20m radius at a speed of 20 m/s the combined mass of the boy and the cycle is 90kg. The angle that the cycle makes with the vertical so that it may not fall is (g=9.8${\scriptstyle{}^{m}/{}_{{{\sec }^{2}}}}$)
A.60.25°
B.63.90°
C.26.12°
D.30.00 °

Answer 1

Hint:In the circular frame of reference the boy experiences two forces namely the gravitational forces i.e mg due to his own weight and centrifugal force due to his motion. A body that travels an equal distance in equal amounts of time along a circular path has a constant speed but not a constant velocity .



Formula used:



Complete answer:
The boy is in motion along a circular path . We know that in a circular motion one experiences a centrifugal force which is directed towards the centre of the circle. Here also since the boy is in a circular motion along the circle it will experience a centrifugal force but here in addition to that of the centrifugal force it will also experience a gravitational force as the body has some mass which is combined mass of the boy and the cycle . Due to this mass only , the gravitational force will act on it downwards having a magnitude of mg.
Now here the boy moves with a constant speed but not with a constant velocity this is because velocity is a vector and hence has magnitude as well as direction and in a circular motion the direction changes as a function of time and so it cannot be constant in a circular motion . Therefore , here the velocity vector can be represented by the formula :
$v$=$\sqrt{Rg\tan \theta }$
${{v}^{2}}=Rg\tan \theta $
$\tan \theta =\frac{{{v}^{2}}}{Rg}$
           = $\frac{20m/s\times 20m/s}{20m\times 90kg\times 9.8m/{{s}^{2}}}$
          =$\begin{align}
  & \frac{400}{20\times 900} \\
 & ={{63.70}^{\circ }} \\
\end{align}$
$\tan \theta \approx {{63.90}^{\circ }}$


Thus, the correct option is option B.






Note:The centripetal force and the centrifugal force are two different kinds of forces acting on a body in a circular motion . The two forces should not be confused with each other as centripetal force acts towards the axis of rotation or centre of curvature while centrifugal force acts along the radius of the circle and directed away from the centre .