
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
161.1k+ views
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 .
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 .
Recently Updated Pages
A steel rail of length 5m and area of cross section class 11 physics JEE_Main

At which height is gravity zero class 11 physics JEE_Main

A nucleus of mass m + Delta m is at rest and decays class 11 physics JEE_MAIN

A wave is travelling along a string At an instant the class 11 physics JEE_Main

The length of a conductor is halved its conductivity class 11 physics JEE_Main

Two billiard balls of the same size and mass are in class 11 physics JEE_Main

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Displacement-Time Graph and Velocity-Time Graph for JEE

Class 11 JEE Main Physics Mock Test 2025

Differentiate between audible and inaudible sounds class 11 physics JEE_Main

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

JEE Advanced 2025: Dates, Registration, Syllabus, Eligibility Criteria and More

Units and Measurements Class 11 Notes: CBSE Physics Chapter 1

Motion in a Straight Line Class 11 Notes: CBSE Physics Chapter 2

NCERT Solutions for Class 11 Physics Chapter 1 Units and Measurements

NCERT Solutions for Class 11 Physics Chapter 2 Motion In A Straight Line
