Question

The coefficient of friction between the tyres and the road is 0.1. The maximum speed with which a cyclist can take a circular turn of radius 3 m without skidding is (Take $\mathrm { g } = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ )

• A. $\sqrt { 15 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$
• B. $\sqrt { 3 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$
• C. $\sqrt { 30 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$
• D. $\sqrt { 10 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$

Answer 1

Answer: (B)

$\sqrt { 3 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$

Answer 2

Here $r = 3 m , \mu = 0.1 , g = 10 m s ^ { - 2 }$

The maximum speed with which a cyclist can take a turn without skidding is

$v _ { \text {max } } = \sqrt { \mu r g } = \sqrt { 0.1 \times ( 3 m ) \left( 10 m s ^ { - 2 } \right) }$

$= \sqrt { 3 } m s ^ { - 1 }$