Question

A boy of mass $30kg$ starts running from rest along a circular path of radius $6m$ with constant tangential acceleration of magnitude $2m{s}^{-1}$. After $2s$ from start he feels that his shoes started slipping on the ground. The friction between his shoes and ground is (Take $g=10m{s}^{-1}$)

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. $\frac{1}{5}$

Answer 1

The correct option is B $\frac{1}{3}$

Given that,

Mass of boy, $m=30kg$

After $2s$, speed of boys, $v=2\times 2=4m/s$

At this moment, centripetal force on the boy is,

$F_c=\frac{m{v}^2}{R}=\frac{30\times 16}{6}=80N$

Tangential force on the boy is ,

$F_t=m{a}_t=30\times 2=60N$

Total force on the boy is,

$F=\sqrt{F_c^2+F_t^2}=\sqrt{{80}^2+{60}^2}=100N$

At the time of slipping, $F=\mu mg$

$⟹100=\mu \times 30\times 10⟹\mu =\frac{1}{3}$