A man is standing on a rough $(\mu = 0.5)$ horizontal disc rotating with constant angular velocity of $5$ $rad/sec.$ At what distance from centre should he stand so that he does not slip on the disc?
$R \leq 0.2m$
$R > 0.2 m$
$R > 0.5 m$
$R > 0.3 m$
A $100 \,kg$ car is moving with a maximum velocity of $9 \,m/s$ across a circular track of radius $30\,m$. The maximum force of friction between the road and the car is ........ $N$
A body of mass $m$ is tied to one end of a spring and whirled round in a horizontal plane with a constant angular velocity. The elongation in the spring is one centimetre. If the angular velocity is doubled, the elongation in the spring is $5\, cm$ . The original length of the spring is ............ $cm$
Write equation of centripetal acceleration and centripetal force for uniform circular motion.
A stone of mass of $16\, kg$ is attached to a string $144 \,m$ long and is whirled in a horizontal circle. The maximum tension the string can withstand is $16$ Newton. The maximum velocity of revolution that can be given to the stone without breaking it, will be ....... $ms^{-1}$
A motorcycle is travelling on a curved track of radius $500\,m$. If the coefficient of friction between road and tyres is $0.5$, the speed avoiding skidding will be ....... $m/s$