Question

a cyclist riding at a speed of 10m/s takes a turn on horizontal circular road of radius 10√3m without skidding. what is the angle of inclination to the vertical

1)15°
2)30°
3)45°
4)60°
​

Answer 1

Answer:

Cyclist rides the bicycle at speed, v=14√3m/s.

radius of circular road , r=20√3m.

Let inclination angle with vertical by cyclist is A.

a normal reaction acts between floor and bicycle.

then at equilibrium,

NsinA=

r

mv²

..........(i)

NcosA=mg.........(ii)

dividing equations (i) by (ii),

tanA=

rg

v

2

now put v=14√3,r=20√3 and g=9.8m/s

so , tanA=

(20√3×9.8)

(14√3)

2

=

196√3

196×3

=

196

196√3

=√3

hence, tanA=√3=tan60°

so, A=60°